Solving a Particle's Spiral Orbit under Central Force

AI Thread Summary
The discussion focuses on deriving the force acting on a particle in a spiral orbit defined by r=a*theta. The user is struggling with an extra factor of 2 in their calculations for the a^2 term while applying the differential equation d^2u/dtheta^2 + u = (-1/ml^2u^2)*f(u^-1). They have computed the second derivative of u with respect to theta but are unable to eliminate the factor of 2. Participants suggest sharing detailed steps to identify potential errors in the calculations. The conversation emphasizes the importance of careful manipulation of equations in solving physics problems.
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Homework Statement


A particle moves under the action of a central force in a spiral orbit given by r=a*theta. Show that the force is f(r) = (-L^2/mr^3)*[1 + (a^2)/(r^2)]


Homework Equations





The Attempt at a Solution


I know how to do the problem, but I keep ending up with a factor of 2 for the a^2 term. Any pointers on how to fix this? Thanks for the help!
 
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Sorry for that... I used the equation d^2u/dtheta^2 + u = (-1/ml^2u^2)*f(u^-1). For the second derivative of u with respect to theta i got 2*a*theta^-3, which i re-wrote as 2*a^2*u^3. I plugged that result into the diff. equation, but was unable to 'get rid of' the factor of 2 for the a^2 term. Any pointers?
 
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