Abstract
One of the most ubiquitous forces in physics is the central force. In any case where a particle possesses a “charge” that couples to a “field”, the field outside the charge is nearly always a radial field if the particle can be considered to be a dimensionless point. Examples include the classical Newtonian law of gravitation, the electrostatic field, and the Yukawa model of the strong nuclear force. The common feature in these examples is a spherically-symmetric potential that depends only on the radial separation from the point-particle source of the field. In this chapter, we will focus on mostly on gravitationally-bound systems.
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- 1.
Alternatively, we can deduce that \(\varvec{\ell }\) is constant by simply noting that for a central potential U(r), the force \(\mathbf {F} = -\mathbf {\nabla }U\) points the radial direction, and hence the torque on the particle about the origin is zero. (See Sect. 1.4, conservation law II.).
- 2.
Since there are no external forces acting on the system, the center-of-mass frame for this problem is an inertial frame.
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Benacquista, M.J., Romano, J.D. (2018). Central Force Problems. In: Classical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-68780-3_4
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DOI: https://doi.org/10.1007/978-3-319-68780-3_4
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