50 1 Lagrange Mechani Az Fig. 1.23 Bead on a rotating parabolic wire in the earth's gravitational field w 111 Exercise 1

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50 1 Lagrange Mechani Az Fig 1 23 Bead On A Rotating Parabolic Wire In The Earth S Gravitational Field W 111 Exercise 1 1 (61.06 KiB) Viewed 35 times

50 1 Lagrange Mechani Az Fig. 1.23 Bead on a rotating parabolic wire in the earth's gravitational field w 111 Exercise 1.2.4 A parabolically curved wire rotates with constant angular velocity w around the 3 axis. On this rotating wire a bead of mass m moves frictionlessly in the earth's gravitational field (g = -ge). If the wire is just within the vz plane (Fig. 1.23) then it holds for the position of the mass wy? (a > 0) 1. Find the constraints! How many degrees of freedom are left? 2. Use cylindrical coordinates (2.4.2) to represent the Lagrangian! 3. Calculate for the special case 208 the Lagrange equations of the second kind and show that (1 + tap) is an integral of motion (conserved quantity