370(3): General Theory of a Rigid Body Subjected to Force and Torque

This theory can be applied to any relevant problem, such as gyroscope motions and Milankovitch cycles. It is shown that the motion is governed by Cartan geometry with spin connection (26) for any situation. Therefore the Euler equations are governed by a special case of Cartan gemetry and can be generalized. The same spin connection can be used to calculate the Cartan torsion and curvature, and to deduce the ECE2 field equations of the motion. The torque vector is defined in general by Eqs. (30) and (31) and the force vector in general by Eqs. (33) and (34). Orbital motion is a special case of Eq. (34). It is possible to solve the torque and force equations with model assumptions, but the Euler Lagrange equations are more elegant, using the general potential (42). The powerful Maxima code can crunch out equations that are completely impossible to solve by hand giving a great deal of information.


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