Spherical motion (motion of a rigid body around a fixed point) is the movement of an absolutely rigid body in which it has one fixed point.
When moving around a fixed point O, each of the points of a solid body describes in space a spherical surface whose center is point O.
When describing the laws of spherical motion, it is customary to use coordinates called Euler angles [1] :
- - angle of own rotation;
- - angle of precession ;
- - angle of nutation .
An example of a spherical motion is the motion of a precessing top or any body swirling around an axis that does not coincide with the axis of the least or greatest moment of inertia. Another example is the movement of points on the teeth of a bevel roller in a bevel gear planetary gear. One of the characteristics of spherical motion is associated with the movement of the apex , the trajectory of which on the unit sphere is studied, in particular, in the dynamics of gyroscopes .
See also
- Translational motion
- Rotational motion
- Difficult movement
- Plane motion
Literature
- Targ S. M. A short course in theoretical mechanics. Textbook for technical colleges. - 10th ed., Rev. and add. - M .: Higher. school., 1986.— 416 s, ill.
- R. Feynman, R. Leighton, M. Sands. Feynman lectures in physics. Tom. 2. The space. Time. Traffic.
Other
An example of rotation of an absolutely rigid body twisted around an axis that does not coincide with the axis of the smallest or greatest moment of inertia is demonstrated by cosmonaut Vladimir Dzhanibekov