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, the determination of orbits from given laws of force.[6] 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.

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${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
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Core topics Damping ratio Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
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Unlike real forces such as electromagnetic forces, fictitious forces do not originate from physical interactions between objects.