THEORETICAL MATRIX STUDY OF RIGID BODY GENERAL MOTION (original) (raw)

THEORETICAL MATRIX STUDY OF RIGID BODY PSEUDO TRANSLATIONAL MOTION

Greener Journal of Physics and Natural Sciences, 2017

In this paper, a pseudo translational motion of free asymmetrical rigid body to an absolute reference system is studied. A private kind of Theorem of change of generalized body impulse is formulated. This theorem is called Theorem of change of pseudo generalized body impulse. A private kind of Condensed Lagrange equations is formulated. These equations are called Condensed Lagrange equations for study of pseudo translational motion of free asymmetrical rigid body. Using that theorem and those equations, the pseudo translational motion of the rigid body is successfully studied. The paper is theoretical, but it gives a base for a number of applications. For example, these are investigations of the motion, stability and management of satellite. The other main application is free or forced small body vibrations. Moreover, the obtained formulas are appropriate for computer numerical integrations by contemporary mathematical programs.

THEORETICAL MATRIX STUDY OF RIGID BODY RELATIVE MOTION

The relative motion of an arbitrary asymmetrical rigid body in this article is studied. Three new additional kinematic characteristics are defined, namely, vectors-real absolute, transmissive and relative generalized velocity. A new theorem for summation of the rigid body real generalized velocities with these new additional kinematic characteristics is formulated. Using the final differential equations of absolute rigid body motion, which have been obtained in previous author's articles, the differential equations describing the rigid body relative motion in a matrix form is obtained. These equations are suitable for numerical solution using specialized mathematical programs.

THEORETICAL MATRIX STUDY OF RIGID BODY ABSOLUTE MOTION

2018

The absolute motion of an arbitrary asymmetric rigid body is studied. This motion is determined after its relative motion has been obtained. The most important peculiarity in this dynamical rigid body model is that the selected pole does not coincide with its mass center. Seven new kinematic characteristics have been defined. The first ones are the following vectors: real absolute, transmisive and relative generalized velocities. The second ones are the vectors-real absolute, transmisive, relative and Coriolisian generalized accelerations. Two new theorems are formulated. The first one is for summation the vectors of real generalized velocities. The second one is for summation the vectors of real generalized accelerations. The system of differential equations describing the rigid body relative motion in matrix form is determined. The algorithm for obtaining the rigid body absolute motion is described.

THEOREM FOR CHANGE OF THE RIGID BODY GENERALIZED IMPULSE

In this conference paper, a rigid body absolute general motion is studied. The rigid body is assumed as homogeneous and unsymmetrical. New additional kinetic characteristics are used. The most important of these are the following: the vector-real generalized velocity of the rigid body, the vector-generalized impulse of the rigid body and the vector-real generalized force of the rigid body. Using these new kinetic characteristics, a new theorem is defined. It is called Theorem for change of the rigid body generalized impulse. With its help, the differential equations in matrix form are obtained. These equations describe the rigid body absolute general motion. Two cases are studied-a pole that coincides and does not coincide with the rigid body mass center. The new theorem enriches the theory of Rigid Body Mechanics. The compact matrix equations provide an excellent opportunity for studying the most complicated dynamic models. They are suitable for numerical solutions with modern mathematical programs such as MatLab, MathCAD and others.

A New Form of Equations for Rigid Body Rotational Dynamics

2014

Original scientific paper In the paper, a new form of differential equations for rigid body attitude dynamics is obtained. Three s-parameters (modified Rodrigues-Hamilton parameters) and three angular velocity parameters are used as unknown variables. Built equations are particularly useful for analytical and numerical study of rotational motion of a rigid body. The topological structure of configurational s-manifold for a balanced rigid body is investigated. An example of the use of constructed equations to describe the rotational motion of a rigid body in a resisting medium is considered.

Analysis methods of the motion of a rigid body about its mass center

sra.ro

The paper presents the results of some numerical applications, obtained by studying the motion of a rigid body about its mass center. The differential equations are determined in two ways: by means of Euler angles and by means of finite rotations, described by the elements of the rotation quaternions. In both cases, Runge-Kutta integration method has been used. The numerical results are compared and conclusions are drawn upon the accuracy of the two ways of describing the motion, as well as upon the numerical integration method. 3 1 3 2 J J J M J J J M J J J M y x Oz z z x Oy y 3 2 1 0 Figure 2. , J J J , J . J J y x 23 Figure 3. , J J J , J J J y x 2 3 1 = = = = J . J J z 5 1 2 = =

General Motion of a Rigid Body

Lecture Notes in Physics, 2009

The time interval minimization of rigid body motion with constant mechanical energy has been considered in this paper. Generalized coordinates are Cartesian's coordinates of mass center and the Euler's angles, which are specified at the initial and the final position. The problem has been solved by the application of the Pontryagin's principle. Finite difference method has been applied in order to obtain the solution of the two-point boundary value problem.

Acceleration analysis of rigid body motion

Journal of Computational and Applied Mechanics

The aim of this paper is to analyze some second order motion properties of rigid body motion. The existence of unique acceleration center is proven by means of vectortensor algebra for the case when the vectors of angular velocity and of angular acceleration are linearly independent. The case when the vectors of angular velocity and of angular acceleration are linearly dependent is also considered. Explicit coordinate free relationships are derived for the position of the acceleration center and axis. A detailed analysis of the linear eigenvalue problem arising in the definition of acceleration axis is presented.

Equivalent problems in rigid body dynamics — I

Celestial Mechanics & Dynamical Astronomy, 1987

The general problem of motion of a rigid body about a fixed point under the action of stationary non-symmetric potential and gyroscopic forces is considered. The equations of motion in the Euler-Poisson form are derived. An interpretation is given in terms of charged, magnetized gyrostat moving in a superposition of three classical fields. As an example, the problem of motion of a satellite — gyrostat on a circular orbit with respect to its orbital system is reduced to that of its motion in an inertial system under additional magnetic and Lorentz forces. When the body is completely symmetric about one of its axes passing through the fixed point, the above problem is found to be equivalent to another one, in which the body has three equal moments of inertia and the forces are symmetric around a space axis. The last problem is well-studied and the given analogy reveals a number of integrable cases of the original problem. A transformation is found, which gives from each of these cases a class of integrable cases depending on an arbitrary function. The equations of motion are also reduced to a single equation of the second order.