Consider two masses m₁ and m² interacting according to a potential V (☎₁ – ☎₂). (a) Write the Lagrangian in terms of the generalized coordinates Rcm = (m₁ři+m₂ř2)/(m₁+ m₂) and r = r₁ – T2, and their derivatives. (b) Using the independence of the Lagrangian with respect to Řcm, find expressions for the conserved total momentum.
Consider two masses m₁ and m² interacting according to a potential V (☎₁ – ☎₂). (a) Write the Lagrangian in terms of the generalized coordinates Rcm = (m₁ři+m₂ř2)/(m₁+ m₂) and r = r₁ – T2, and their derivatives. (b) Using the independence of the Lagrangian with respect to Řcm, find expressions for the conserved total momentum.
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Transcribed Image Text:Consider two masses m₁ and m² interacting according to a potential V (☎₁ – ☎₂).
(a) Write the Lagrangian in terms of the generalized coordinates Rcm = (m₁ři+m₂ř2)/(m₁+
m₂) and r = 7₁ – 72, and their derivatives.
(b) Using the independence of the Lagrangian with respect to Řcm, find expressions for
the conserved total momentum.
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