369(8): General Theory of the Gyroscope and Milankovitch Cycles

The gyro in the presence of a general external torque (4), generating the potential energy (2), is given by solving the lagrangian (14). If there is no interaction between the rotation of the gyroscope and the translation of its fixed point, the problem is solved by Eqs. (21) to (24), in which (24) is independent. This means that there is simple force on the gyro’s point, giving the external torque (4). However if U is a function of r and theta, Eqs. (21), (22), (24) and (26) must be solved simultaneously, giving a lot more information. The Milankovitch cycles are given by solving Eqs. (29) to (31), and the orbital motion in a plane by solving Eqs. (34) to (36). If for some reason condition (37) holds, then the Milankovitch cycles are affected in a way to be determined by the Maxima code. So I will proceed to write up Sections 1 and 2 of UFT369.


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