Alan Whitman - Profile on Academia.edu (original) (raw)
Papers by Alan Whitman
Asymptotic Solution and Trajectory Planning for Open-Loop Control of Mobile Robots
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Mar 10, 2017
A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dy... more A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dynamic solution and trajectory planning. The method is based on quantification of sliding by a small nondimensional parameter. Asymptotic expansion of the equations yields the dominant nonslip solution along with a first-order correction for sliding. A trajectory planning is then introduced based on transitional circles between the robot initial states and target reference trajectory. The transitional trajectory ensures smooth convergence of the robot states to the target reference trajectory, which is essential for open-loop control. Experimental results with a differential drive mobile robot demonstrate the significant improvement of the controller performance when the first-order correction is included.
Power and Refrigeration
Mechanical engineering series, 2023
Work and Heat
Mechanical engineering series, 2023
Measurement and Properties of Matter
Mechanical engineering series, 2023
Entropy and the Second Law
Mechanical Engineering Series
Characteristics of plasma probes in an MHD WORKING fluid
Theory of electrostatic probes in high pressure plasma, discussing ionization and recombination p... more Theory of electrostatic probes in high pressure plasma, discussing ionization and recombination phenomena, diffusion boundary layer, spherical probe, etc
Equilibrium
Mechanical Engineering Series, Dec 5, 2019
Mechanical engineering series, 2023
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Equilibrium
Mechanical engineering series, 2023
Journal of Applied Physics, 1976
The stability of electric arc discharges has been explored through the use of an energy balance c... more The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible.
Applications of the two-scale embedding technique
wprm, Aug 1, 1993
A Simulation Relation for Flat-Plate Hydrodynamic Impact
Journal of Ship Research, 1973
A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic im... more A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic impact problem due to "trapped air." For large plates this becomes a similarity relation so that it is possible to scale impacts.
Non-Isoplanatic Effects In Imaging Through Turbulent Media
Optical, Infrared, Millimeter Wave Propagation Engineering, 1988
We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging us... more We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging using intensity interferometry. For conventional imaging, we treat both short- and long-time exposures. In imaging using intensity interferometry, we present a general result, in which isoplanicity is not assumed, and then study the first order non-isoplanatic correction. Explicit calculations are given for the correction under typical atmospheric conditions.
Tenure waves
Journal of the Franklin Institute, 1975
On The Lateral Stability of a Flexible Truck
Journal of Dynamic Systems, Measurement, and Control, 1983
Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets bas... more Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.
Limit Cycle Behavior of a Flexible Truck
Journal of Applied Mechanics, 1987
We calculate the variation in critical speed of a flexible truck as a function of limit cycle amp... more We calculate the variation in critical speed of a flexible truck as a function of limit cycle amplitude and truck parameters (i.e., shear and bending stiffnesses, and truck geometry), by means of a perturbation procedure. We find that the creep force nonlinearity is dominant, and that it can cause the nonlinear critical speed to be either lower or higher than the linear critical speed, depending on the values of the two stiffnesses.
Aspect Ratio Effects on the Added-Mass of a Slender Pulsating Cylinder
Journal of Applied Mechanics, 1972
We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit le... more We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit length of a finite length, slender, cylinder vibrating in the breathing mode. We find, to dominant order in the expansion, that when the wavelength of the vibration is smaller than the half length, the added mass is independent of the aspect ratio while in the antithetical case it is solely dependent on that quantity.
Irradiance Fluctuations and the Assumption of Gaussian Statistics for a Beam Propagating in a Random Medium
Journal of Modern Optics, 1976
In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a... more In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.
Mechanical Engineering Series, 2019
The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is ... more The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is meant to indicate a rate, and W F is a derived dimension [E]), we call it the power developed by the force. When the power developed is positive, we say that the force generates power, and when it is negative, we say that it absorbs power. The natural units for power are kg m 2 /s 3 in the SI, and lbm ft 2 /s 3 in the English System.
Measurement and Properties of Matter
Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies... more Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies move under the action of the forces and moments that are exerted on them. Thermodynamics is the theory that integrates dynamics with the concept of temperature. Dynamics is a fundamental part of physics because of Newton’s second law, which describes how the momentum of a fixed quantity of matter evolves in time.
Asymptotic Solution and Trajectory Planning for Open-Loop Control of Mobile Robots
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Mar 10, 2017
A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dy... more A novel open-loop control method is presented for mobile robots based on an asymptotic inverse dynamic solution and trajectory planning. The method is based on quantification of sliding by a small nondimensional parameter. Asymptotic expansion of the equations yields the dominant nonslip solution along with a first-order correction for sliding. A trajectory planning is then introduced based on transitional circles between the robot initial states and target reference trajectory. The transitional trajectory ensures smooth convergence of the robot states to the target reference trajectory, which is essential for open-loop control. Experimental results with a differential drive mobile robot demonstrate the significant improvement of the controller performance when the first-order correction is included.
Power and Refrigeration
Mechanical engineering series, 2023
Work and Heat
Mechanical engineering series, 2023
Measurement and Properties of Matter
Mechanical engineering series, 2023
Entropy and the Second Law
Mechanical Engineering Series
Characteristics of plasma probes in an MHD WORKING fluid
Theory of electrostatic probes in high pressure plasma, discussing ionization and recombination p... more Theory of electrostatic probes in high pressure plasma, discussing ionization and recombination phenomena, diffusion boundary layer, spherical probe, etc
Equilibrium
Mechanical Engineering Series, Dec 5, 2019
Mechanical engineering series, 2023
The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge... more The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro-and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.
Equilibrium
Mechanical engineering series, 2023
Journal of Applied Physics, 1976
The stability of electric arc discharges has been explored through the use of an energy balance c... more The stability of electric arc discharges has been explored through the use of an energy balance coupled with charge conservation. In order to facilitate this analysis, a new model for the electrical conductivity function has been proposed. Asymptotic solutions for the arc governing equations have been obtained. Stability criteria have been developed from both the linear theory (infinitesimal size disturbance) and from a minimizing solution point of view for finite size disturbances. The results delineate an open region in the stability diagram where arc instabilities may be possible.
Applications of the two-scale embedding technique
wprm, Aug 1, 1993
A Simulation Relation for Flat-Plate Hydrodynamic Impact
Journal of Ship Research, 1973
A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic im... more A correlation is presented of the maximum pressure that obtains in the flat-plate hydrodynamic impact problem due to "trapped air." For large plates this becomes a similarity relation so that it is possible to scale impacts.
Non-Isoplanatic Effects In Imaging Through Turbulent Media
Optical, Infrared, Millimeter Wave Propagation Engineering, 1988
We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging us... more We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging using intensity interferometry. For conventional imaging, we treat both short- and long-time exposures. In imaging using intensity interferometry, we present a general result, in which isoplanicity is not assumed, and then study the first order non-isoplanatic correction. Explicit calculations are given for the correction under typical atmospheric conditions.
Tenure waves
Journal of the Franklin Institute, 1975
On The Lateral Stability of a Flexible Truck
Journal of Dynamic Systems, Measurement, and Control, 1983
Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets bas... more Analytic formulae for the critical speed and frequency of an interconnected pair of wheelsets based on an asymptotic expansion in a truck geometric parameter are derived. No restriction is placed on the values of either the shear or bending stiffness; consequently, the entire structure of the stability surface is obtained. The surface is a symmetric function of the two dimensionless stiffnesses and it depends predominantly on their series combination. Expressions are obtained for the local and global extrema and their locations. The frequency varies monotonically from the wheelset kinematic frequency to the rigid truck frequency as a function of stiffness. The results are compared with numerical solutions and found to be accurate in the region of physically obtainable values of the expansion parameter.
Limit Cycle Behavior of a Flexible Truck
Journal of Applied Mechanics, 1987
We calculate the variation in critical speed of a flexible truck as a function of limit cycle amp... more We calculate the variation in critical speed of a flexible truck as a function of limit cycle amplitude and truck parameters (i.e., shear and bending stiffnesses, and truck geometry), by means of a perturbation procedure. We find that the creep force nonlinearity is dominant, and that it can cause the nonlinear critical speed to be either lower or higher than the linear critical speed, depending on the values of the two stiffnesses.
Aspect Ratio Effects on the Added-Mass of a Slender Pulsating Cylinder
Journal of Applied Mechanics, 1972
We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit le... more We derive, by means of an asymptotic analysis, a simple expression for the added mass per unit length of a finite length, slender, cylinder vibrating in the breathing mode. We find, to dominant order in the expansion, that when the wavelength of the vibration is smaller than the half length, the added mass is independent of the aspect ratio while in the antithetical case it is solely dependent on that quantity.
Irradiance Fluctuations and the Assumption of Gaussian Statistics for a Beam Propagating in a Random Medium
Journal of Modern Optics, 1976
In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a... more In a previous paper [1] we obtained an asymptotic expression for the irradiance fluctuations of a finite beam propagating in a random medium in the strong-scattering case (i.e. the characteristic diffraction length is large compared to the characteristic scattering length). The solution was given as the product of a plane wave portion and a finite beam correction. We show here that if the statistics of the fluctuations of the infinite and finite beams are assumed to be gaussian (in which case the fourth-order coherence function may be expressed in terms of second-order coherence functions), then the finite beam result obtained is in disagreement with our previous result. Consequently, we conclude that the statistics of a finite beam cannot be gaussian. However, assuming that the statistics of the infinite beam are gaussian leads to no contradiction. This result is an indication of the importance of finite beam size effects in irradiance fluctuation studies.
Mechanical Engineering Series, 2019
The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is ... more The quantityẆ F is a derived dimension [E/t] = [FL/t] = [ML 2 /t 3 ] (the dot over the symbol is meant to indicate a rate, and W F is a derived dimension [E]), we call it the power developed by the force. When the power developed is positive, we say that the force generates power, and when it is negative, we say that it absorbs power. The natural units for power are kg m 2 /s 3 in the SI, and lbm ft 2 /s 3 in the English System.
Measurement and Properties of Matter
Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies... more Dynamics, as you have learned in previous courses, is the study of how particles and rigid bodies move under the action of the forces and moments that are exerted on them. Thermodynamics is the theory that integrates dynamics with the concept of temperature. Dynamics is a fundamental part of physics because of Newton’s second law, which describes how the momentum of a fixed quantity of matter evolves in time.