11.3. Lagrangian Formulation

Try these first

1. 1.

   What is the Lagrangian of a system? Provide its basic formula.

   Hint

   Remember the basic energy definitions.

2. 2.

   What does the Euler-Lagrange equation help us find?

   Hint

   Think about what governs motion.

3. 3.

   What is the formula for the Lagrangian?

   Hint

   Recall the definitions of T and V.

4. 4.

   True or False: The Lagrangian formulation only applies to mechanical systems without external forces.

   • True
   • False

   Hint

   Think about forces acting on robotic systems.

5. 5.

   For a robotic arm with three joints, derive the full Lagrangian in terms of the angles and link lengths. Compute the equations of motion.

   Hint

   Break down the energies step-by-step for each joint and remember that each part contributes to L.

6. 6.

   Analyze a simple pendulum using the Lagrangian method. Identify T and V, and derive its equation of motion.

   Hint

   Consider how to express height in terms of the angle θ of the pendulum.