A particle of mass m moves under an attractive central force mk/r^a where r is the radial distance from the force centre O.
assuming that the radial and transverse components of accleration in polar coordinated (r, (-)) are (r''-r*(-)'^2) and (2r'*(-)' + r*(-)'') respectively, show that the differential equation for the orbit is,
d^2u/d(-)^2 = k/h^2 * u^(a-2)
where u=1/r and h=r^2 * (-)
sorry about the notations, i wasn't sure how to present the equation on this.
I am having trouble with this and a similar question. I am not sure how to derive the differential equation for the radial and transverse components.
p.s i hope this is the right sub-forum to post in