Tessellate S.T.E.M.S - Physics - College - Set 3 - Problem 1

Classical Mechanics Level 3

Lagrangian of a system is given by $\mathcal{L} = \frac{1}{2}m\dot{q}^2 + 3 \lambda q^2 \cos (q) \dot{q} - \lambda q^3 \sin (q) \dot{q}$ . Suppose at time $t=0$ we have $q(0) = 0$ and $\dot{q}(0) = 1$ , then find the coordinate q at $t=1$ .

This problem is a part of Tessellate S.T.E.M.S.

1 0

\cos{1}

\sin{1}

1 solution

Tristan Goodman
Apr 21, 2019

Applying the Euler-Lagrange equations to the given Lagrangian results in the second and third terms cancelling out and the equation of motion for the system is just m(d^2q/dt^2)=0 or ma=0. The given initial conditions then allow us to conclude that (dq/dt)=v=1 and q=q.

Tessellate S.T.E.M.S - Physics - College - Set 3 - Problem 1

1 solution

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