(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.
(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.
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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(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.
(b)
Introduce a dissipative term in the equation of motion assuming that the
dissipative force acting on a particle is proportional to the partical velocity with the coefficient of
proportionality v. Write down the modified equation of motion.
From the dimensionless equation of motion modified by dissipation
Compare to question (2 b)
derive a linearised equation of motion around a stable equilibrium state. Solve it
and determine what is the range of values of the free parameter B for which the particle motion is
oscillatory or non-oscillatory? What is the critical value of that determines a transition from the
subcritical case with the oscillatory motion to the super-critical case with the non-oscillatory
motion?
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