Chapter 16
3-Dimensional Kinetics of a Rigid Body
Moments et produit de l’inertie
The moment of inertia for a differential element of a rigid body can be calculated by multiplying the mass of the element by the square of the shortest ...
Tenseur d’inertie
The inertia tensor is used to describe the distribution of mass and rotational inertia of a rigid body.
The inertia tensor is represented using a 3×3 ...
Moment d’inertie autour d’un axe arbitraire
The moment of inertia is commonly discussed in relation to principal axes, but it can also be calculated for any arbitrary axis.
When considering an ...
Moment angulaire autour d’un axe arbitraire
Consider a rigid body of mass 'm' and a center of mass at point G, rotating in an inertial reference frame.
At an arbitrary point P, the angular ...
Moment angulaire et principaux axes d’inertie
The angular momentum for a rigid body can be expressed as the integral of the cross-product of the position vector of the mass element with the ...
Principe de l’impulsion et du moment
Consider a rigid body undergoing a general planar motion, a combination of translational and rotational motion.
Newton's second law gives the equation ...
Énergie cinétique pour un corps rigide
Consider a rigid body undergoing a general planar motion. Its center of mass is located at point G.
The kinetic energy of the i-th particle of the rigid ...
Équation du mouvement d’un corps rigide
The motion of a rigid body can be described using equations for translational motion and rotational motion about the center of mass.
Newton's Second ...
Équations du mouvement d’Euler
Consider a rigid body rotating with an angular velocity of ω in an inertial frame of reference.
Another rotating frame is attached to the body that ...
Mouvement sans couple
Torque-free motion refers to the movement of a rigid body without any external torques acting upon it.
Consider an axisymmetric object, with the z-axis ...
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