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11: Conservative two-body Central Forces

Last updated

Nov 21, 2020
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- 10.S: Nonconservative systems (Summary)
- 11.1: Introduction to Conservative two-body Central Forces

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11.1: Introduction to Conservative two-body Central Forces
Conservative, central, two-body central forces are important in physics because of the pivotal role that Coulomb and gravitational forces play in nature. Therefore this chapter focusses on the physics of systems involving conservative two-body central forces.
11.2: Equivalent one-body Representation for two-body motion
The equations for relative motion of two bodies interacting via two-body central forces can be represented by an equivalent one-body problem simplifying the mathematics.
11.3: Angular Momentum
Angular momentum is an important conserved quantity.
11.4: Equations of Motion
Equations of motion.
11.5: Differential Orbit Equation
Differential orbit equation. Binet coordinate transformation.
11.6: Hamiltonian
Hamiltonian for conserved two-body central forces.
11.7: General Features of the Orbit Solutions
General features of the orbit solutions for two-body forces.
11.8: Inverse-square, two-body, central force
Inverse-square, two-body, central force. Eccentricity vector.
11.9: Isotropic, linear, two-body, central force
Isotropic, linear, two-body, central force. Symmetry tensor.
11.10: Closed-orbit Stability
Closed-orbit stability. Bertrands theorem.
11.11: The Three-Body Problem
The three body problem. Planar approximation and the restricted three-body approximation.
11.12: Two-body Scattering
Two-body scattering cross-sections. Rutherford scattering.
11.13: Two-body kinematics
Two-body kinematics. Velocities, angles, kinetic energies, solid angles, optimum detection of the scattered two bodies.
11.E: Conservative two-body Central Forces (Exercises)
11.S: Conservative two-body Central Forces (Summary)

Thumbnail: Two bodies with a major difference in mass orbiting a common barycenter internal to one body (similar to the Earth–Moon system). (Public Domain; Zhatt).

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