# Mechanics of Planar Particle Motion

Mechanics Of Planar Particle Motion

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, the determination of orbits from given laws of force. This article is focused more on the kinematical issues surrounding planar motion, that is, 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.

Read more about Mechanics Of Planar Particle Motion:  Analysis Using Fictitious Forces, Moving Objects and Observational Frames of Reference, Fictitious Forces in A Local Coordinate System, Fictitious Forces in Polar Coordinates, Fictitious Forces in Curvilinear Coordinates

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Mechanics Of Planar Particle Motion - Fictitious Forces in Curvilinear Coordinates - "State-of-motion" Versus "coordinate" Fictitious Forces
... in an inertial frame of reference are called in this article the "state-of-motion" fictitious forces and those that originate from differentiation in a particular coordinate system are called "coordinate ... Using the expression for the acceleration above, Newton's law of motion in the inertial frame of reference becomes where F is the net real force on the particle ... No "state-of-motion" fictitious forces are present because the frame is inertial, and "state-of-motion" fictitious forces are zero in an inertial frame, by definition ...

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