Unformatted text preview: ˙ θ ˙ y 1 = a (cos ϕ ) ˙ ϕ + l 2 (cos θ ) ˙ θ ˙ x 2 =a (sin ϕ ) ˙ ϕ + l 2 (sin θ ) ˙ θ ˙ y 2 = a (cos ϕ ) ˙ ϕl 2 (cos θ ) ˙ θ The kinetic energy T = m ( ˙ x 2 1 + ˙ y 2 1 + ˙ x 2 2 + ˙ y 2 2 ) / 2 becomes T = m ( a 2 ˙ ϕ 2 + l 2 4 ˙ θ 2 ) while the potential energy is equal to zero. Lagrange equations read ¨ ϕ = 0 , ¨ θ = 0 or ˙ ϕ = ω 1 = const ˙ θ = ω 2 = const Note that this independence of ϕ and θ motions happens only because we considered the particles of identical masses. Otherwise the energy T would have had a term proportional to ˙ ϕ · ˙ θ . 1...
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 Fall '11
 Bazaliy
 mechanics, Energy, Kinetic Energy, Mass, Work, φ

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