Mechanics of planar particle motion information

Mechanics of planar particle motion^[1] is the analysis of the motion of particles gravitationally attracted to one another observed from non-inertial reference frames^[2]^[3]^[4] and the generalisation of this problem to planetary motion.^[5] This type of analysis is closely related to centrifugal force, two-body problem, orbit and Kepler's laws of planetary motion. The mechanics of planar particle motion fall in the general field of analytical dynamics, and helps determine orbits from the given force laws.^[6] This article is focused more on the kinematic issues surrounding planar motion, which are the determination of the forces necessary to result in a certain trajectory given the particle trajectory.

General results presented in fictitious forces 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). With this, 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.

^ See for example, John Joseph Uicker; Gordon R. Pennock; Joseph Edward Shigley (2003). Theory of Machines and Mechanisms. Oxford University Press. p. 10. ISBN 0-19-515598-X., Harald Iro (2002). A Modern Approach to Classical Mechanics. World Scientific. p. Chapter 3 and Chapter 4. ISBN 981-238-213-5.
^ Fictitious forces (also known as pseudo forces, inertial forces or d'Alembert forces), exist for observers in a non-inertial reference frame. See, for example, Max Born & Günther Leibfried (1962). Einstein's Theory of Relativity. New York: Courier Dover Publications. pp. 76–78. ISBN 0-486-60769-0. inertial forces., NASA: Accelerated Frames of Reference: Inertial Forces, Science Joy Wagon: Centrifugal force - the false force Archived 2018-08-04 at the Wayback Machine
^ Jerrold E. Marsden; Tudor S. Ratiu (1999). Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Springer. p. 251. ISBN 0-387-98643-X.
^ John Robert Taylor (2004). Classical Mechanics. Sausalito CA: University Science Books. p. Chapter 9, pp. 327 ff. ISBN 1-891389-22-X.
^ Florian Scheck (2005). Mechanics (4th ed.). Birkhäuser. p. 13. ISBN 3-540-21925-0.
^ Edmund Taylor Whittaker (1988). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies (Fourth edition of 1936 with a foreword by Sir William McCrea ed.). Cambridge University Press. p. Chapter 1, p. 1. ISBN 0-521-35883-3.

[planar-1] See for example, John Joseph Uicker; Gordon R. Pennock; Joseph Edward Shigley (2003). Theory of Machines and Mechanisms. Oxford University Press. p. 10. ISBN 0-19-515598-X., Harald Iro (2002). A Modern Approach to Classical Mechanics. World Scientific. p. Chapter 3 and Chapter 4. ISBN 981-238-213-5.

[fictitious-2] Fictitious forces (also known as pseudo forces, inertial forces or d'Alembert forces), exist for observers in a non-inertial reference frame. See, for example, Max Born & Günther Leibfried (1962). Einstein's Theory of Relativity. New York: Courier Dover Publications. pp. 76–78. ISBN 0-486-60769-0. inertial forces., NASA: Accelerated Frames of Reference: Inertial Forces, Science Joy Wagon: Centrifugal force - the false force Archived 2018-08-04 at the Wayback Machine

[Marsden-3] Jerrold E. Marsden; Tudor S. Ratiu (1999). Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Springer. p. 251. ISBN 0-387-98643-X.

[Taylor1-4] John Robert Taylor (2004). Classical Mechanics. Sausalito CA: University Science Books. p. Chapter 9, pp. 327 ff. ISBN 1-891389-22-X.

[Scheck-5] Florian Scheck (2005). Mechanics (4th ed.). Birkhäuser. p. 13. ISBN 3-540-21925-0.

[Whittaker1-6] Edmund Taylor Whittaker (1988). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies (Fourth edition of 1936 with a foreword by Sir William McCrea ed.). Cambridge University Press. p. Chapter 1, p. 1. ISBN 0-521-35883-3.

Mechanics of planar particle motion information

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