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Dynamics of rigid bodies

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Dynamics of rigid bodies
  • Moment of Inertia
  • Principal axes
  • Time dependence
Moment of Inertia
The angular momentum in a moving coordinate system is given by:
angular momentum in a moving coordinate system

where I is the moment of inertia with respect to a central axis, which is given by:
moment of inertia

or, in the continuous case:
moment of inertia

Further holds:


Steiner’s theorem is: if axis C axis D.


Moment of Inertia
Object Moment of Inertia Object Moment of Inertia
Cavern cylinder Moment of Inertia of Cavern cylinder Massive cylinder Moment of Inertia of Massive cylinder
Disc, axis in plane disc through m Moment of Inertia of Disc, axis in plane disc through m Halter Moment of Inertia of Halter
Cavern sphere Moment of Inertia of Cavern sphere Massive sphere Moment of Inertia of Massive sphere
Bar, axis through c.o.m. Moment of Inertia of bar Bar, axis through end Moment of Inertia of bar
Rectangle, axis plane thr. c.o.m. Moment of Inertia of Rectangle Rectangle, axis b thr. m Moment of Inertia of Rectangle


Principal axes
Each rigid body has (at least) 3 principal axes which stand to each other. For a principal axis holds:


The following holds: with


Time dependence
For torque of force torque holds:



The torque torque is defined by:
 
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