Mechanics of planar particle motion

This article describes a particle in planar motion[1] when observed from non-inertial reference frames.[2][3][4] 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.[5] 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.[6] 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.

This article's tone or style may not reflect the encyclopedic tone used on Wikipedia. (November 2022)

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${\displaystyle {\textbf {F}}={\frac {\mathrm {d} }{\mathrm {d} t}}(m{\textbf {v}})}$ Second law of motion
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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.