Kinematics (from the French term cinématique, coined by the physicist André-Marie Ampère from the greek κίνημα -ατος, kinema -atos = “movement”, derived in turn from the verb κινέω, kineo = “to move”) is that branch of Newtonian mechanics that deals with quantitatively describing the motion of bodies, using only the notions of space and time, regardless of the causes (forces) of the motion itself, task instead of dynamics.
Modern kinematics was born with the studies of Galileo Galilei, but its modern definition, which uses the principles of infinitesimal calculus, can be dated to the speech of Pierre Varignon on January 20, 1700 before the Royal Academy of Sciences in Paris. In the second half of the eighteenth century is enriched by the contributions of Jean Le Rond d’Alembert and André-Marie Ampère. With the Theory of Relativity by Albert Einstein in 1905 begins the relativistic kinematics.
The definition of kinematics as “geometry of motion” is correct for a description of motion in the context of relativity theory, but can also be accepted for a classical description, since the relativistic and classical scheme coincide in almost all common cases. Depending on whether the body in motion is a material point, a rigid system, a deformable system, etc., it is referred to as kinematics of the point, kinematics of rigid systems, kinematics of deformable systems, etc.
To study the motion of a body means to determine instant by instant the position of each of its points with respect to a prefixed reference system and this can be done in many cases with simple rules, when we know the motion of one or more points of the body.
The study of relative motion, i.e., of the laws of motion defined by two observers moving with respect to each other, is the subject of relative kinematics; it is based on the two postulates that it is possible to determine an absolute time independent of the observer and that the distance between two fixed points is also independent of the relative motion of the observers.
These postulates are valid in the most common cases, as shown by experience, but are no longer valid when the relative speed of the observers is close to that of light. The description of motion is then the subject of relativistic kinematics of which the relative kinematics is a special case corresponding to consider infinite the speed of light.