Q-1. Consider a simple pendulum of mass m and length I as shown in the figure. (a) Write down the (unconstrained) Lagrangian of the system in terms of r(t) and 0(t). (b) Obtain the Lagrange's multiplier equations for r(t) and 0(t) and de- termine the value of the Lagrange undetermined multiplier A. ө т (c) Find the force of constraint Ř. What is the physical interpretation of Ř (or A)?
Q-1. Consider a simple pendulum of mass m and length I as shown in the figure. (a) Write down the (unconstrained) Lagrangian of the system in terms of r(t) and 0(t). (b) Obtain the Lagrange's multiplier equations for r(t) and 0(t) and de- termine the value of the Lagrange undetermined multiplier A. ө т (c) Find the force of constraint Ř. What is the physical interpretation of Ř (or A)?
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Transcribed Image Text:Q-1. Consider a simple pendulum of mass m and length I as shown in
the figure.
(a) Write down the (unconstrained) Lagrangian of the system in terms
of r(t) and 0(t).
(b) Obtain the Lagrange's multiplier equations for r(t) and 0(t) and de-
termine the value of the Lagrange undetermined multiplier A.
ө
т
(c) Find the force of constraint Ř. What is the physical interpretation of
Ř (or A)?
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