I read some explanations of precession; this side for example summarizes briefly almost all what I have understood so far.

But one thing bothers me: Following all this formulas, the precession velocity is constant as long as the external torque is applied constantly. So let there be a spinning disk without external torque (so no precession, the rotations axis keeps its direction). If I now start to apply some constant torque to change the rotation axis, does the precession velocity jump instantaneously to the calculated, constant value? Is there no "precession acceleration phase" or something?

  • $\begingroup$ Hi I could be wrong, but I don't think any classical effect could occur instantaneously...anybody got any example to say they do? regards $\endgroup$ – user74893 Mar 18 '15 at 13:16
  • $\begingroup$ Thats exactly what i am thinking, but I cannot find anything describing the acceleration of the rotation axis' movement. $\endgroup$ – Horstling Mar 18 '15 at 14:12
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    $\begingroup$ How do you start to apply a constant torque without a torque ramp-up phase? $\endgroup$ – ja72 Mar 18 '15 at 15:20

Behind the precession motion are the dynamics of the body; primarily its moments of inertia. And just as you cannot have 'instant' velocity when you apply a force to an inertial body, you also cannot have instant precessional (angular) velocity. Inertia prohibits this and so yes there is angular acceleration.

The angular rate of precession can be calculated from the gyroscopic equations of motion, and the solution will contain the matrix of moments of inertia that govern these rates of change.

Your hypothetical spinning disk is only an idealization, and in the real physical world, nothing is perfectly non-dissipating of energy, and so as the non-perfect disk spins it will create its own disturbing torque that will lead to precession, even in the absence of gravitational fields. The ultimate state of stability depends on whether the body is a 'flat' or otherwise narrow spinner.

  • $\begingroup$ "The angular rate of precession can be calculated from the gyroscopic equations of motion". That's true and I understand that part, but can you give me some hints how to derive formulas for calculating the mentioned acceleration towards this angular rate of precession? $\endgroup$ – Horstling Mar 18 '15 at 16:21

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