2 Kinematics of a particle trajectory in a non-rotating frame of reference.In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and working in reverse, using kinematic synthesis to design a mechanism for a desired range of motion. Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. They are also central to dynamic analysis. Geometric transformations, also called rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of the equations of motion. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies.
For further details, see analytical dynamics. The study of how forces act on bodies falls within kinetics, not kinematics. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.
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