Mecanica Analitica Nivaldo-1 4

Problema L.4\nX = Rβ + Rsenβ → x = R(β + senβ)\ny = Rcosβ → y = R(L - cosβ)\nx' = R(β - θcosβ)\ny' = R·θsinθ\nT = m (x'² + y'²)\n = \n2\n v = -mgy\n = -mgR(L - cosβ)\nT = mR² (2θ̇² - 2β̇²cosθ)\n = \n2\nT = 2mR²sen²(β)θ̇²\nL = 2mR²sen(2θ)θ̇² + mgR(L - cosβ)\n = \n2\nL = 8mR²θ̇² + 2mgR(L - ϵ)\n16mR²θ̇² + 74mgB₄ → 0\n ü = -g u\n 4R\nu(t) = A cos(ωt) + B sen(ωt) ω = √(g/µR) T = 2π/ω