Can You Solve for R in Terms of t Using This Integral?

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The discussion revolves around solving an integral related to the motion of a point mass under a non-standard force law, specifically an inverse cubic law. Participants express confusion about the variables involved, particularly the definitions of R, theta, and u, and how they relate to the integral. The conversation shifts to the conservation of energy and angular momentum, emphasizing the need to express R as a function of theta rather than time. There is a focus on deriving the equation of the orbit and integrating the resulting expressions, with participants seeking clarification on the potential energy associated with the force. Ultimately, the integral is crucial for determining the orbit shape based on energy and angular momentum.
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Odyssey said:
t-t_{0}=\int_{R_{0}}^{R(t)}\frac{du}{\sqrt{2mEL^{-2}u^4-u^2-2mL^{-2}u^4V(u)}}

where, u = R of theta. So should I plug the V = -(1/2)Amr^-2 into V(u)? :confused:

Now I have the integral. plug the V = -(1/2)Amr^-2 into V(u)? How should I proceed from here? :confused:

Thank you again for the help!
 

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