Many thanks again! This illustrates the checking method used by Horst and myself for about a decade in several hundred papers and books, and sometimes the calculations are also checked by computer by Doug Lindstrom. The correct result will of course be used in the final paper. So Eq. (8) of Note 370(7) just sent over must be corrected for this extra term found by Maxima. It does not affect the main conclusions of the note.
Sent: 15/02/2017 12:14:59 GMT Standard Time
Subj: Re: 370(6): General Transformation from Spherical Polar to Eulerian Angles
The computer gives an additional term in eq. 4, see protocol.
Am 14.02.2017 um 12:23 schrieb EMyrone:
This is given by Eq. (4) in general, and in the special case (5), by Eq. (6). It is difficult to find this transformation in the literature, but it is very useful. The lagrangian of rotational dynamics in terms of the Euler angles can always be transformed to a simpler lagrangian expressed in terms of spherical polar coordinates. For a spherical top of moment of inertia I = I1 = I2 = I3, the rotational kinetic energy is Eq. (4) multiplied on both sides by I. It is seen that the number of lagrange variables is reduced from three to two, and the Euler Lagrange equations of motion are greatly simplified. Then, gravitational terms can be added as in Horst’s dumbbell representation of the earth in orbit around the sun.