(a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x)=-4/x+B/x² where x is the particle displacement in m. (d) Mimimise the number of independent parameters in the modified equation of motion with dissipation by introducing dimensionless varibles and r for x and r. (e) Present the equation derived in the form of an energy balance equation and find the expressions for the effective kinetic and potential energies (T and V), and dissipative function F.
(a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x)=-4/x+B/x² where x is the particle displacement in m. (d) Mimimise the number of independent parameters in the modified equation of motion with dissipation by introducing dimensionless varibles and r for x and r. (e) Present the equation derived in the form of an energy balance equation and find the expressions for the effective kinetic and potential energies (T and V), and dissipative function F.
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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Question
Transcribed Image Text:(a)
Write down the equation of motion for the point particle of mass m moving in
the Kepler potential U(x) = -A/x+ B/x² where x is the particle displacement in m.
(d)
Mimimise the number of independent parameters in the modified equation of
motion with dissipation by introducing dimensionless varibles and r for x and r.
(e)
Present the equation derived in the form of an energy balance equation and
find the expressions for the effective kinetic and potential energies (7 and V), and dissipative
function F.
Expert Solution
Step 1: Determine the given variables
According to our guidelines,we can do only first three sub parts. Kindly repost other subpart as the next question.
We have to find the equation of motion and minimize the number of independent parameters and energy stability equation
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