A locomotive of mass M moves on a frictionless rail. Inside the locomotive is a simple pendulum of length l and mass m. Let the acceleration of gravity be constant and its value g. Also assume that the angle is very small (θ << 1). In this case, the expansion will be made in the Lagrangian expression, including the terms of 2. So sin (θ) ≈ θ can be written as cos (θ) ≈ 1- θ2 / 2. Let X be the displacement in the horizontal direction. a) Write the Lagrangian of the system in terms of generalized coordinates X and θ. b) Write the equations of motion of the system.
A locomotive of mass M moves on a frictionless rail. Inside the locomotive is a simple pendulum of length l and mass m. Let the acceleration of gravity be constant and its value g. Also assume that the angle is very small (θ << 1). In this case, the expansion will be made in the Lagrangian expression, including the terms of 2. So sin (θ) ≈ θ can be written as cos (θ) ≈ 1- θ2 / 2. Let X be the displacement in the horizontal direction. a) Write the Lagrangian of the system in terms of generalized coordinates X and θ. b) Write the equations of motion of the system.
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A locomotive of mass M moves on a frictionless rail. Inside the locomotive is a simple pendulum of
length l and mass m. Let the acceleration of gravity be constant and its value g. Also assume that the
angle is very small (θ << 1). In this case, the expansion will be made in the Lagrangian expression,
including the terms of 2.
So sin (θ) ≈ θ can be written as cos (θ) ≈ 1- θ2 / 2.
Let X be the displacement in the horizontal direction.
a) Write the Lagrangian of the system in terms of generalized coordinates X and θ.
b) Write the equations of motion of the system.
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