Mechanics of planar particle motion

rdf:langString Mechanics of planar particle motion

rdf:langString vertical

rdf:langString Velocity vector v, always tangent to the path of motion.

rdf:langString Acceleration vector a, not parallel to the radial motion but offset by the angular and Coriolis accelerations, nor tangent to the path but offset by the centripetal and radial accelerations.

rdf:langString Position vector r, always points radially from the origin.

rdf:langString November 2013

rdf:langString Acceleration vector plane polar coords.svg

rdf:langString Position vector plane polar coords.svg

rdf:langString Velocity vector plane polar coords.svg

rdf:langString Should this be a Prime instead of an apostrophe?

rdf:langString This article describes a particle in planar motion when observed from non-inertial reference frames. The most famous examples of planar motion are related to the motion of two spheres that are gravitationally attracted to one another, and the generalization of this problem to planetary motion. See centrifugal force, two-body problem, orbit and Kepler's laws of planetary motion. Those problems fall in the general field of analytical dynamics, determining orbits from the given force laws. This article is focused more on the kinematical issues surrounding planar motion, that is, the determination of the forces necessary to result in a certain trajectory given the particle trajectory. General results presented in fictitious forces here are applied to observations of a moving particle as seen from several specific non-inertial frames, for example, a local frame (one tied to the moving particle so it appears stationary), and a co-rotating frame (one with an arbitrarily located but fixed axis and a rate of rotation that makes the particle appear to have only radial motion and zero azimuthal motion). The Lagrangian approach to fictitious forces is introduced. Unlike real forces such as electromagnetic forces, fictitious forces do not originate from physical interactions between objects.