The discussion focuses on demonstrating that the motion of a particle under a central force defined by F = -kr results in an elliptical orbit. The equations of motion are derived as m d²x/dt² = -kx and m d²y/dt² = -ky, leading to the solutions x = Acos(ωt + βx) and y = Bsin(ωt + βy). The phase constants βx and βy are assumed to be zero for simplification, which is a valid approach for analyzing the system's motion.
PREREQUISITESStudents of physics, particularly those studying classical mechanics, as well as educators and anyone interested in the mathematical modeling of particle motion under central forces.
Yes, except why assume the phase constants are zero?GeoStudy said:Homework Statement
I just need a hint. So we are given:
F = -kr
We are asked:
Show that:
(a) The orbit is an ellipse with the force center at the center of the ellipse.
Homework Equations
I guess we break it up into its components:
The Attempt at a Solution
m d2x/dt2 = -kx => x = Acos(ωt + βx)
m d2y/dt2 = -ky => y= Bsin(ωt + βy)
where βx = βy = 0