On the transitivity equations of rigid-body dynamics
Abstract
This paper presents direct derivations of the various forms of the famous transitivity equations of rigid-body kinematics from a simple and unified viewpoint. These forms are indispensable in the derivation of the Eulerian (gyro) equations of motion via the Lagrangian (analytical mechanics) method. Both true (holonomic) and quasi (nonholonomic) coordinate forms are presented. A vectorial derivation of the Eulerian equations from the Central Equation and from Hamilton's Principle is also includced in the Appendix.
- Publication:
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ASME Journal of Applied Mechanics
- Pub Date:
- December 1992
- Bibcode:
- 1992ATJAM..59..955P
- Keywords:
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- Euler-Lagrange Equation;
- Rigid Structures;
- Rotating Bodies;
- Body Kinematics;
- Euler Equations Of Motion;
- Hamiltonian Functions;
- Vectors (Mathematics);
- Physics (General)