Kinematics of a Point Particle

Abstract

Kinematics analyzes the trajectories, velocities, and accelerations of the points of a moving body, the deformations of its volume elements, and the dependence of all these quantities on the frame of reference. In many cases, when such an accurate description of motion is too complex, it is convenient to substitute the real body with an ideal body for which the analysis of the preceding characteristics is simpler, provided that the kinematic description of the ideal body is sufficiently close to the behavior of the real one. For instance, when the deformations undergone by a body under the influence of the acting forces can be neglected, we adopt the rigid body model, which is defined by the condition that the distances among its points do not change during the motion. More particularly, if the body is contained in a sphere whose radius is much smaller than the length of its position vectors relative to a frame of reference, then the whole body is sufficiently localized by the position of any one of its points. In this case, we adopt the model of a point particle. In this chapter we analyze the kinematics of a point particle defining velocity, acceleration, trajectory, and compound motion.