kinematica

Kinematics, or kinematica in some languages, is the branch of classical mechanics that describes the motion of objects without considering the forces that cause that motion. It focuses on the geometric and temporal relationships among position, velocity, and acceleration, using coordinate systems and reference frames to express how an object's state changes with time.

Key concepts include displacement (a vector), speed (a scalar), velocity (vector), and acceleration (vector). The motion of a particle is represented by its position vector r(t); its velocity is v = dr/dt and its acceleration a = d^2r/dt^2. For one-dimensional motion with constant acceleration: s = ut + 1/2 at^2 and v^2 = u^2 + 2as, where u is initial velocity. In multiple dimensions, these relations apply componentwise.

Rotational kinematics treats angular position theta, angular velocity omega = dtheta/dt, and angular acceleration alpha = domega/dt; for a point at distance r from the rotation axis, tangential velocity is v_t = r omega and tangential acceleration a_t = r alpha, with a centripetal component a_r = r omega^2.

Kinematics also covers planar and spatial motion, curvilinear trajectories, and the motion of rigid bodies where orientation changes over time. Relative motion considers the motion of one object as observed from another frame.

Applications appear in projectile analysis, robotics, animation, biomechanics, automobile safety, and spaceflight. Kinematics provides the descriptive foundation for dynamics, which explains how forces produce motion. The subject traces its roots to Galileo and Descartes, with formal development in Newtonian mechanics and ongoing extensions to relativistic kinematics.

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