Gerassimos Manoussakis | National Technical University of Athens (original) (raw)
Papers by Gerassimos Manoussakis
Table 2, page 592 “Normal gravity on the geoid” becomes “Normal gravity on the ellipsoid”. ... more Table 2, page 592
“Normal gravity on the geoid” becomes “Normal gravity on the ellipsoid”.
The related formula stays the same, only the index “geoid” is changed to “ellipsoid”.
The relation r > R becomes r >= R
AppliedMath (Feature Paper), 2024
The G-modified Helmholtz equation is a partial differential equation that enables us to express g... more The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of the second-order partial derivatives of the unknown quantity equal to zero) is used to express the Earth’s gravity potential (disturbing and normal potential) in order to represent other useful quantities—which are also known as functionals of the disturbing potential—such as gravity disturbance,
gravity anomaly, and geoid undulation as a series of spherical harmonics. We demonstrate that by using the G-modified Helmholtz equation, not only gravity intensity but also disturbing potential and its functionals can be expressed as a series of spherical harmonics.
Having gravity intensity represented as a series of spherical harmonics allows us to create new Global Gravity Models. Furthermore, a more detailed examination of the Earth’s isogravitational surfaces is conducted.
Finally, we tabulate our results, which makes it clear that new Global Gravity Models for gravity intensity g will be very useful for many geophysical and geodetic applications.
Book Publisher International (a part of SCIENCEDOMAIN International), May 10, 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria. Some criteria indicate the perception of certifying organizations, of countries that apply them, and of the hotel industry, as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. Hotel classification systems are tools for maintaining the high quality of hotel industry. Also, ?he classification of hotels presents heterogeneity. Common points are the range of ranking categories and the marks used, but if the requirements of the criteria of each category are analyzed, very different conditions are discovered, sometimes even within the same country. Nevertheless, the introduction of a classification system for hotels is a complex matter due to the diversity of classification systems, accommodation types and the cultural, environmental and economic context in which the systems operate each time in individual countries. This study results, in a proposed model hotel classification system, which will directly contribute to reducing the risk of not meeting customers' expectations and providing hotel services more efficiently, depending on the type and category of accommodation. Effective management of customer expectations is crucial to ensuring the viability of the tourism business. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.
Mathematics, issue 11, 4362, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Mathematics, issue 11, 1974, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Acta Geodaetica et Geophysica, 2013
The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second ord... more The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second order partial derivatives of the normal potential, expressed in a local Cartesian coordinate system. With the help of the Eötvös matrix it is possible to determine the variation of the normal gravity vector locally around a point P. In addition, the Eötvös matrix contains information about equipotential surfaces and the curvature of the plumbline. In this work we present a method to estimate the elements of the Eötvös matrix at an arbitrary point P above the ellipsoid, whose geometrical height is low. Under this condition, it is shown that the second order partial derivatives of the normal potential vary linearly along the line vertical to the ellipsoid and passing through P. It is worth mentioning that the proposed method to estimate the elements of the Eötvös matrix is much simpler than by following the definition of the matrix. In addition, it will be shown that if Q is the projection of P along the plumbline to the ellipsoid, then the values of the Eötvös matrix elements at point P are strongly related with plumbline curvature and the principal curvatures at Q. Finally, simple relations about plumbline curvature and the gradient of the normal gravity vector at point P will be presented.
Contributions to Geophysics and Geodesy, 2017
The components of the Eötvös matrix are useful for various geodetic applications, such as interpo... more The components of the Eötvös matrix are useful for various geodetic applications, such as interpolation of the elements of the deflection of the vertical, determination of gravity anomalies and determination of geoid heights. A torsion balance instrument is customarily used to determine the Eötvös components. In this work, we show that it is possible to estimate the Eötvös components at a point on the Earth’s physical surface using gravity measurements at three nearby points, comprising a very small network. In the first part, we present the method in detail, while in the second part we demonstrate a numerical example. We conclude that this method is able to estimate the components of the Eötvös matrix with satisfactory accuracy.
Current Approaches in Science and Technology Research Vol. 4, 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria. Some criteria indicate the perception of certifying organizations, of countries that apply them, and of the hotel industry, as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. Hotel classification systems are tools for maintaining the high quality of hotel industry. Also, ?he classification of hotels presents heterogeneity. Common points are the range of ranking categories and the marks used, but if the requirements of the criteria of each category are analyzed, very different conditions are discovered, sometimes even within the same country. Nevertheless, the introduction of a classification system for hotels is a complex matter due to the diversity of classification systems, accommodation types and the cultural, environmental and economic context in which the systems operate each time in individual countries. This study results, in a proposed model hotel classification system, which will directly contribute to reducing the risk of not meeting customers' expectations and providing hotel services more efficiently, depending on the type and category of accommodation. Effective management of customer expectations is crucial to ensuring the viability of the tourism business. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.
Journal of Applied Geology and Geophysics, volume 9, issue 3, series 1 , 2021
The vertical gradient of normal gravity (VGNG) plays a significant role in several applications a... more The vertical gradient of normal gravity (VGNG) plays a significant role in several applications and is an interesting quantity from a pure theoretical point of view as well. In this work the VGNG will be studied from a theoretical point of view, therefore the expression of the VGNG at a point P on the Earth's physical surface in geodetic coordinates is presented. Since the value VGNG also depends on the mean curvature of the normal equipotential surfaces, an effort has been made to express the fundamental quantities E U , F U , G U , L U , M U and N U at point P in a specific form. These quantities are expressed as combinations of the fundamental quantities of the ellipsoid of revolution, its mean curvature, Gauss curvature, and normal reduction. The fundamental quantities of the ellipsoid of revolution are determined at a point Q which is the projection of a point P, on the ellipsoid along the vertical line. The fundamental quantities of the ellipsoid, its mean curvature and Gauss curvature and the geometric height of the chosen point P represent the geometric part of the quantities E U
The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second ord... more The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second order partial derivatives of the normal potential, expressed in a local Cartesian coordinate system. With the help of the Eötvös matrix it is possible to determine the variation of the normal gravity vector locally around a point P. In addition, the Eötvös matrix contains information about equipotential surfaces and the curvature of the plumbline. In this work we present a method to estimate the elements of the Eötvös matrix at an arbitrary point P above the ellipsoid, whose geometrical height is low. Under this condition, it is shown that the second order partial derivatives of the normal potential vary linearly along the line vertical to the ellipsoid and passing through P. It is worth mentioning that the proposed method to estimate the elements of the Eötvös matrix is much simpler than by following the definition of the matrix. In addition, it will be shown that if Q is the projection of P along the plumbline to the ellipsoid, then the values of the Eötvös matrix elements at point P are strongly related with plumbline curvature and the principal curvatures at Q. Finally, simple relations about plumbline curvature and the gradient of the normal gravity vector at point P will be presented.
The components of the Eötvös matrix are useful for various geodetic applications, such as interpo... more The components of the Eötvös matrix are useful for various geodetic applications, such as interpolation of the elements of the deflection of the vertical, determination of gravity anomalies and determination of geoid heights. A torsion balance instrument is customarily used to determine the Eötvös components. In this work, we show that it is possible to estimate the Eötvös components at a point on the Earth's physical surface using gravity measurements at three nearby points, comprising a very small network. In the first part, we present the method in detail, while in the second part we demonstrate a numerical example. We conclude that this method is able to estimate the components of the Eötvös matrix with satisfactory accuracy.
The elements of the Eötvös matrix, usually determined by torsion balance measurements, are useful... more The elements of the Eötvös matrix, usually determined by torsion balance measurements, are useful in many geodetic applications. We present a method for the computation of the elements of the normal Eötvös matrix at a point on the Earth's physical surface, resulting in an improvement in the determination of the deflection of the vertical at intermediate points of a network. In the process, we also present analytical expressions for the computation of the components of the deflection of the vertical. From those expressions and using also a numerical example, we show that the proposed refinement is not completely negligible.
This paper presents an approach to determine the gradient of curvature of the normal plumblines a... more This paper presents an approach to determine the gradient of curvature of the normal plumblines at a point P above the ellipsoid and introduces a new geometrical object which is the isocurvature line. The assumed facts are the coordinates of the point P and the formula for the normal gravity potential U. For the determination of the gradient of the normal plumbline curvature k at the point P we define a small circle on the meridian plane of P whose center is at the point P. The circle has the radius of ε = 1 m and interior D. In this circle we construct a function k a to approximate the curvature function k. The function k a is a quotient of polynomials hence it is easy to find its partial derivatives at the point P i.e. grad k a (P). For the construction of the function k a we make the assumption that in the interior of the circle D the first order partial derivatives of U behave linearly and the second order partial derivatives have constant values which equal their value at the point P and then we set grad k(P) = grad k a (P). An isocurvature line of the normal gravity field passing through a point P is a curve ā such that the value of the function of the plumblines' curvature k is constant and equals k(P). We give a formula to find the direction of the isocurvature line on the meridian plane and we prove that there are infinitely many isocurvature lines passing through the point P and they all lie on a special surface, the isocurvature surface.
A neutral direction of a gravity field is a direction along which the components of the gravity v... more A neutral direction of a gravity field is a direction along which the components of the gravity vector remain locally unchanged. A neutral point is a point at which there exists a neutral direction. This research will focus on the neutral directions for the normal gravity vector. The necessary condition for the existence of neutral directions at an arbitrary point P above the ellipsoid is that the determinant of the Eötvös matrix must be equal to zero. The slopes of these directions depend on the value of the principal curvatures and the curvature of the plumbline. In all cases the neutral directions lie on the meridian plane at point P. An interesting case is when the vertical gradient of normal gravity is equal to zero. Finally in the last two paragraphs we show that neutral points are not isolated in the three dimensional space and give a numerical example for the case of a spherical gravity field.
International Journal of Scientific Research and Innovative Technology , 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria.Some criteria indicate the perception of certification organizations, countries that apply them, and the hotel industry as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.
Table 2, page 592 “Normal gravity on the geoid” becomes “Normal gravity on the ellipsoid”. ... more Table 2, page 592
“Normal gravity on the geoid” becomes “Normal gravity on the ellipsoid”.
The related formula stays the same, only the index “geoid” is changed to “ellipsoid”.
The relation r > R becomes r >= R
AppliedMath (Feature Paper), 2024
The G-modified Helmholtz equation is a partial differential equation that enables us to express g... more The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of the second-order partial derivatives of the unknown quantity equal to zero) is used to express the Earth’s gravity potential (disturbing and normal potential) in order to represent other useful quantities—which are also known as functionals of the disturbing potential—such as gravity disturbance,
gravity anomaly, and geoid undulation as a series of spherical harmonics. We demonstrate that by using the G-modified Helmholtz equation, not only gravity intensity but also disturbing potential and its functionals can be expressed as a series of spherical harmonics.
Having gravity intensity represented as a series of spherical harmonics allows us to create new Global Gravity Models. Furthermore, a more detailed examination of the Earth’s isogravitational surfaces is conducted.
Finally, we tabulate our results, which makes it clear that new Global Gravity Models for gravity intensity g will be very useful for many geophysical and geodetic applications.
Book Publisher International (a part of SCIENCEDOMAIN International), May 10, 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria. Some criteria indicate the perception of certifying organizations, of countries that apply them, and of the hotel industry, as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. Hotel classification systems are tools for maintaining the high quality of hotel industry. Also, ?he classification of hotels presents heterogeneity. Common points are the range of ranking categories and the marks used, but if the requirements of the criteria of each category are analyzed, very different conditions are discovered, sometimes even within the same country. Nevertheless, the introduction of a classification system for hotels is a complex matter due to the diversity of classification systems, accommodation types and the cultural, environmental and economic context in which the systems operate each time in individual countries. This study results, in a proposed model hotel classification system, which will directly contribute to reducing the risk of not meeting customers' expectations and providing hotel services more efficiently, depending on the type and category of accommodation. Effective management of customer expectations is crucial to ensuring the viability of the tourism business. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.
Mathematics, issue 11, 4362, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Mathematics, issue 11, 1974, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Acta Geodaetica et Geophysica, 2013
The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second ord... more The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second order partial derivatives of the normal potential, expressed in a local Cartesian coordinate system. With the help of the Eötvös matrix it is possible to determine the variation of the normal gravity vector locally around a point P. In addition, the Eötvös matrix contains information about equipotential surfaces and the curvature of the plumbline. In this work we present a method to estimate the elements of the Eötvös matrix at an arbitrary point P above the ellipsoid, whose geometrical height is low. Under this condition, it is shown that the second order partial derivatives of the normal potential vary linearly along the line vertical to the ellipsoid and passing through P. It is worth mentioning that the proposed method to estimate the elements of the Eötvös matrix is much simpler than by following the definition of the matrix. In addition, it will be shown that if Q is the projection of P along the plumbline to the ellipsoid, then the values of the Eötvös matrix elements at point P are strongly related with plumbline curvature and the principal curvatures at Q. Finally, simple relations about plumbline curvature and the gradient of the normal gravity vector at point P will be presented.
Contributions to Geophysics and Geodesy, 2017
The components of the Eötvös matrix are useful for various geodetic applications, such as interpo... more The components of the Eötvös matrix are useful for various geodetic applications, such as interpolation of the elements of the deflection of the vertical, determination of gravity anomalies and determination of geoid heights. A torsion balance instrument is customarily used to determine the Eötvös components. In this work, we show that it is possible to estimate the Eötvös components at a point on the Earth’s physical surface using gravity measurements at three nearby points, comprising a very small network. In the first part, we present the method in detail, while in the second part we demonstrate a numerical example. We conclude that this method is able to estimate the components of the Eötvös matrix with satisfactory accuracy.
Current Approaches in Science and Technology Research Vol. 4, 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria. Some criteria indicate the perception of certifying organizations, of countries that apply them, and of the hotel industry, as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. Hotel classification systems are tools for maintaining the high quality of hotel industry. Also, ?he classification of hotels presents heterogeneity. Common points are the range of ranking categories and the marks used, but if the requirements of the criteria of each category are analyzed, very different conditions are discovered, sometimes even within the same country. Nevertheless, the introduction of a classification system for hotels is a complex matter due to the diversity of classification systems, accommodation types and the cultural, environmental and economic context in which the systems operate each time in individual countries. This study results, in a proposed model hotel classification system, which will directly contribute to reducing the risk of not meeting customers' expectations and providing hotel services more efficiently, depending on the type and category of accommodation. Effective management of customer expectations is crucial to ensuring the viability of the tourism business. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.
Journal of Applied Geology and Geophysics, volume 9, issue 3, series 1 , 2021
The vertical gradient of normal gravity (VGNG) plays a significant role in several applications a... more The vertical gradient of normal gravity (VGNG) plays a significant role in several applications and is an interesting quantity from a pure theoretical point of view as well. In this work the VGNG will be studied from a theoretical point of view, therefore the expression of the VGNG at a point P on the Earth's physical surface in geodetic coordinates is presented. Since the value VGNG also depends on the mean curvature of the normal equipotential surfaces, an effort has been made to express the fundamental quantities E U , F U , G U , L U , M U and N U at point P in a specific form. These quantities are expressed as combinations of the fundamental quantities of the ellipsoid of revolution, its mean curvature, Gauss curvature, and normal reduction. The fundamental quantities of the ellipsoid of revolution are determined at a point Q which is the projection of a point P, on the ellipsoid along the vertical line. The fundamental quantities of the ellipsoid, its mean curvature and Gauss curvature and the geometric height of the chosen point P represent the geometric part of the quantities E U
The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second ord... more The normal Eötvös matrix is a three dimensional symmetric matrix. Its elements are the second order partial derivatives of the normal potential, expressed in a local Cartesian coordinate system. With the help of the Eötvös matrix it is possible to determine the variation of the normal gravity vector locally around a point P. In addition, the Eötvös matrix contains information about equipotential surfaces and the curvature of the plumbline. In this work we present a method to estimate the elements of the Eötvös matrix at an arbitrary point P above the ellipsoid, whose geometrical height is low. Under this condition, it is shown that the second order partial derivatives of the normal potential vary linearly along the line vertical to the ellipsoid and passing through P. It is worth mentioning that the proposed method to estimate the elements of the Eötvös matrix is much simpler than by following the definition of the matrix. In addition, it will be shown that if Q is the projection of P along the plumbline to the ellipsoid, then the values of the Eötvös matrix elements at point P are strongly related with plumbline curvature and the principal curvatures at Q. Finally, simple relations about plumbline curvature and the gradient of the normal gravity vector at point P will be presented.
The components of the Eötvös matrix are useful for various geodetic applications, such as interpo... more The components of the Eötvös matrix are useful for various geodetic applications, such as interpolation of the elements of the deflection of the vertical, determination of gravity anomalies and determination of geoid heights. A torsion balance instrument is customarily used to determine the Eötvös components. In this work, we show that it is possible to estimate the Eötvös components at a point on the Earth's physical surface using gravity measurements at three nearby points, comprising a very small network. In the first part, we present the method in detail, while in the second part we demonstrate a numerical example. We conclude that this method is able to estimate the components of the Eötvös matrix with satisfactory accuracy.
The elements of the Eötvös matrix, usually determined by torsion balance measurements, are useful... more The elements of the Eötvös matrix, usually determined by torsion balance measurements, are useful in many geodetic applications. We present a method for the computation of the elements of the normal Eötvös matrix at a point on the Earth's physical surface, resulting in an improvement in the determination of the deflection of the vertical at intermediate points of a network. In the process, we also present analytical expressions for the computation of the components of the deflection of the vertical. From those expressions and using also a numerical example, we show that the proposed refinement is not completely negligible.
This paper presents an approach to determine the gradient of curvature of the normal plumblines a... more This paper presents an approach to determine the gradient of curvature of the normal plumblines at a point P above the ellipsoid and introduces a new geometrical object which is the isocurvature line. The assumed facts are the coordinates of the point P and the formula for the normal gravity potential U. For the determination of the gradient of the normal plumbline curvature k at the point P we define a small circle on the meridian plane of P whose center is at the point P. The circle has the radius of ε = 1 m and interior D. In this circle we construct a function k a to approximate the curvature function k. The function k a is a quotient of polynomials hence it is easy to find its partial derivatives at the point P i.e. grad k a (P). For the construction of the function k a we make the assumption that in the interior of the circle D the first order partial derivatives of U behave linearly and the second order partial derivatives have constant values which equal their value at the point P and then we set grad k(P) = grad k a (P). An isocurvature line of the normal gravity field passing through a point P is a curve ā such that the value of the function of the plumblines' curvature k is constant and equals k(P). We give a formula to find the direction of the isocurvature line on the meridian plane and we prove that there are infinitely many isocurvature lines passing through the point P and they all lie on a special surface, the isocurvature surface.
A neutral direction of a gravity field is a direction along which the components of the gravity v... more A neutral direction of a gravity field is a direction along which the components of the gravity vector remain locally unchanged. A neutral point is a point at which there exists a neutral direction. This research will focus on the neutral directions for the normal gravity vector. The necessary condition for the existence of neutral directions at an arbitrary point P above the ellipsoid is that the determinant of the Eötvös matrix must be equal to zero. The slopes of these directions depend on the value of the principal curvatures and the curvature of the plumbline. In all cases the neutral directions lie on the meridian plane at point P. An interesting case is when the vertical gradient of normal gravity is equal to zero. Finally in the last two paragraphs we show that neutral points are not isolated in the three dimensional space and give a numerical example for the case of a spherical gravity field.
International Journal of Scientific Research and Innovative Technology , 2021
The present research investigates the official classification systems in order to find common, im... more The present research investigates the official classification systems in order to find common, important sectors and criteria.Some criteria indicate the perception of certification organizations, countries that apply them, and the hotel industry as to what is important for a hotel to offer. Official classification systems state their basic principles, which differ from one system to another and not all are met at the same time. Most countries give three reasons for entering a formal rating system: consumer protection, tourism planning and marketing. The study will present the practices applied in the hotel industry, through compliance with official classification systems. It will contribute to the existing knowledge of hoteliers, institutions and organizations that create hotel certification systems, and in general to the knowledge of the tourism industry. The survey data were drawn from the analytical recording and processing of 39 classification systems, applied in different countries and continents.