Numerical Solution of the Motion of a Gyro

All this is very interesting indeed, all solutions of the motion of a gyro that I have found make approximations, both on the classical and quantum levels. Of course Lagrange had no access to computers so would also have used approximations.

To: EMyrone@aol.com
Sent: 23/01/2017 12:21:01 GMT Standard Time
Subj: Re: Final Version of the Last Note

Eqs.(5-7) are a complete set of Lagrange equations that can be solved numerically. I will see if I can do this with Maxima directly, it contains a numerical equation solver of coupled ordinary diff. equations as I realized about one year ago. This can avoid own coding work.

First I will plot the graphs psi dot(theta), phi dot(theta), theta dot dot(theta). One should see some features of the solution then hopefully.

For further work two cases are most interesting:

1. applying an external constant lift velocity in Z direction,
2. applying an external constant torque around Z axis, operating on angle phi.

Horst

Am 23.01.2017 um 13:06 schrieb EMyrone:

OK thanks, Note 368(6) is the correct version to be checked by computer algebra. The problem in general is exceedingly intricate because of the structure of Eq. (5)in which theta = theta(t). This equation (5) should be checked by computer algebra. The others are given by Marion and Thornton. The new Euler Lagrange equation is equation (2), which gives Eq. (5). Eqs. (6) and (7) are given by Marion and Thornton.

In a message dated 23/01/2017 09:27:04 GMT Standard Time, mail writes:

I quickly checked the analytical solution of eq.(29), it is a growing exponential function, whatever that means. I will await the final note for further analysis.

Horst

Am 23.01.2017 um 10:03 schrieb EMyrone:

I will be sending out a final version of the last note, and as usual my hand calculations will be checked using Maxima by co author Horst Eckardt. The hand calculations are used to get an idea of the problem, and this is the method in every UFT paper to which computer algebra can be applied. So there will be virtually no chance of any human error and it will be all a matter of interpretation. The notes should be regarded as sketches for the final painting.

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