The discussion centers on solving for the radius R in terms of time t using an integral related to the motion of a point mass m under a net force F = -Amr^-3. Participants clarify that R is a function of the angle θ, and the integral provided is crucial for determining the orbit of the mass. The conversation highlights the importance of using angular momentum and energy conservation principles to express R as a function of θ, ultimately leading to the integral t - t₀ = ∫(θ₀ to θ(t)) (m/L) R²(u) du. The correct approach involves switching the independent variable from time t to angle θ for effective integration.
PREREQUISITESStudents and professionals in physics, particularly those focused on classical mechanics, orbital dynamics, and mathematical methods in physics. This discussion is also beneficial for anyone working with differential equations in the context of motion under varying forces.
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)?