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(U = m_1 g y_1 + m_2 g y_2 \approx -m_1 g L_1(1-\theta_1^2/2) - m_2 g [L_1(1-\theta_1^2/2) + L_2(1-\theta_2^2/2)]). Drop constants: (U \approx \frac12 (m_1+m_2)g L_1 \theta_1^2 + \frac12 m_2 g L_2 \theta_2^2). lagrangian mechanics problems and solutions pdf
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: A comprehensive textbook-style PDF that includes sections on the calculus of variations, geodesics, and charged-particle motion. Lagrangian Mechanics Problem Solutions - Scribd
[ \ddotr - \omega^2 r = 0 \quad \Rightarrow \quad r(t) = A e^\omega t + B e^-\omega t ]