Unformatted text preview: l 1 = l 2 = l , φ 1 = φ and φ 2 = ψ .) 1. Deﬁne angles φ and ψ for the pendula with respect to the gravity direction and write down the Lagrange function. 2. Derive the equations of motion for small oscillations around the rest position φ = ψ = 0. (Small oscillations neglect all terms in the Taylor expansion of the Lagrangian, which are higher than quadratic in combinations of φ, ˙ φ, ψ, ˙ ψ .) Due Friday, September 16 before class (10 points). (9a) Assume a bilinear kinetic Energy T = X j,k a jk ˙ q j ˙ q k and prove X i ˙ q i ∂T ∂ ˙ q i = 2 T . Due in class (2 points). (9b) Generalized Momentum: Calculate ∂L ∂ ˙ x i , i = 1 , 2 , 3 , for L = 1 2 m~v 2V ( ~x ) . Due in class (2 points)....
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 Fall '11
 berg
 mechanics, Kinetic Energy, Work, Lagrangian mechanics, 3D conservative force, Read LandauLifshitz

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