Name the laws on which the algorithm for solving problems in dynamics is based.

The content of Newton’s first law is reduced to the statement about the existence of inertial reference systems. There are such frames of reference, relative to which the bodies, not subject to external influences, either are at rest, or move uniformly and rectilinearly. Such systems are called inertial reference frames.
I. Newton formulated an important law of motion, named in his honor by Newton’s second law. The force acting on a body in an inertial frame of reference is equal to the product of the body’s mass by the acceleration imparted by this force. Newton’s third law describes the interaction of two bodies (material points). The forces with which two bodies act on each other are equal in magnitude and directed along one straight line in opposite directions.