14.3 : 粒子系の線形力積と運動量の原理

Consider a system of particles moving relative to an inertial frame of reference.

The equation of motion for such a system can be written as the sum of external forces acting on each particle.

Since the internal forces between particles occur in equal and opposite collinear pair, they are excluded from the equation.

Integrating the equation of motion and substituting the limits yields the equation for the principle of linear impulse and momentum for the system of particles.

This principle states that the initial linear momentum of the system, combined with the impulses of all external forces from the initial to the final time, equals the final linear momentum of the system.

Now, consider the equation of the system's center of mass. Differentiating it, the total linear momentum of the particles can be related to the linear momentum of the center of mass.

This relationship is then substituted into the equation for linear impulse and momentum.

The modified equation implies the applicability of the principle to the system of particles that compose a rigid body.