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${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
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Kinematics is a subfield of physics and mathematics, 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.^[1][2][3] Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of both applied and pure mathematics since it can be studied without considering the mass of a body or the forces acting upon it.^[4][5][6] 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. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.

Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics,^[7] 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.

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. They are also central to dynamic analysis.

Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. 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.^[8] In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism.

Etymology

The term kinematic is the English version of A.M. Ampère's cinématique,^[9] which he constructed from the Greek κίνημα kinema ("movement, motion"), itself derived from κινεῖν kinein ("to move").^[10][11]

Kinematic and cinématique are related to the French word cinéma, but neither are directly derived from it. However, they do share a root word in common, as cinéma came from the shortened form of cinématographe, "motion picture projector and camera", once again from the Greek word for movement and from the Greek γρᾰ́φω grapho ("to write").^[12]

Kinematics of a particle trajectory in a non-rotating frame of reference

Particle kinematics is the study of the trajectory of particles. The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x-axis and north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0 m, −50 m, 0 m). If the tower is 50 m high, and this height is measured along the z-axis, then the coordinate vector to the top of the tower is r = (0 m, −50 m, 50 m).

In the most general case, a three-dimensional coordinate system is used to define the position of a particle. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient. All observations in physics are incomplete without being described with respect to a reference frame.

The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin. In three dimensions, the position vector ${\displaystyle {\bf {r}}}$ can be expressed as

where ${\displaystyle x}$, ${\displaystyle y}$, and ${\displaystyle z}$ are the Cartesian coordinates and ${\displaystyle {\hat {\mathbf {x} }}}$, ${\displaystyle {\hat {\mathbf {y} }}}$ and ${\displaystyle {\hat {\mathbf {z} }}}$ are the unit vectors along the ${\displaystyle x}$, ${\displaystyle y}$, and ${\displaystyle z}$ coordinate axes, respectively. The magnitude of the position vector ${\displaystyle \left|\mathbf {r} \right|}$ gives the distance between the point ${\displaystyle \mathbf {r} }$ and the origin. The direction cosines of the position vector provide a quantitative measure of direction. In general, an object's position vector will depend on the frame of reference; different frames will lead to different values for the position vector.

The trajectory of a particle is a vector function of time, ${\displaystyle \mathbf {r} (t)}$, which defines the curve traced by the moving particle, given by

where ${\displaystyle x(t)}$, ${\displaystyle y(t)}$, and $$Zdroj:https://en.wikipedia.org?pojem=Kinematics
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