16.6 : 衝動と瞬間の原理

Consider a rigid body undergoing a general planar motion, a combination of translational and rotational motion.

Newton's second law gives the equation of translational motion for a rigid body. Multiplying it with time interval dt and integrating it over the limits of the integration yields an equation for the principle of linear impulse.

The principle of linear impulse articulates that the change in momentum of an object is directly proportional to the impulse exerted on it. This equation can be represented using three rectangular components.

On the other hand, the equation for rotational motion can be written as the time derivative of the product of the moment of inertia about the center of mass of the object and its angular velocity.

Here, the moment of inertia is constant; transforming this equation into an integral form results in the principle of rotational impulse.

Here, the product of the moment of inertia and the angular velocity of the rigid body is equal to the angular momentum, which can be depicted using three rectangular components.