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Suppose that the gravitational force is not give by the inverse-square law, and instead is F grav = (+) where A and B are real constants. Derive the equations of motion and determine whether angular momentum is conserved. By using the substitution r = 1/u, trans- form the radial component of the equations of motion into a differential equation for u as a function of the angular coordinate 0. Determine for what values of A, B, and integration constants stationary solutions exist and whether they are stable.

Suppose that the gravitational force is not give by the inverse-square law, and instead is F grav = (+) where A and B are real constants. Derive the equations of motion and determine whether angular momentum is conserved. By using the substitution r = 1/u, trans- form the radial component of the equations of motion into a differential equation for u as a function of the angular coordinate 0. Determine for what values of A, B, and integration constants stationary solutions exist and whether they are stable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that the gravitational force is not give by the inverse-square law, and instead is F grav = (+) where A and B are real constants. Derive the equations of motion and determine whether angular momentum is conserved. By using the substitution r = 1/u, trans- form the radial component of the equations of motion into a differential equation for u as a function of the angular coordinate 0. Determine for what values of A, B, and integration constants stationary solutions exist and whether they are stable.
Transcribed Image Text:Suppose that the gravitational force is not give by the inverse-square law, and instead is F grav = (+) where A and B are real constants. Derive the equations of motion and determine whether angular momentum is conserved. By using the substitution r = 1/u, trans- form the radial component of the equations of motion into a differential equation for u as a function of the angular coordinate 0. Determine for what values of A, B, and integration constants stationary solutions exist and whether they are stable.
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