(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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