Consider a system with the following Lagrangian: L = a(i² ² sin² y + y²) + b(i cos y + 2)², where a and b are constants. a) Find the equations of motion for the system. b) Calculate and identify the conserved quantities. Is this system integrable? c) Calculate the energy function for the system.
Consider a system with the following Lagrangian: L = a(i² ² sin² y + y²) + b(i cos y + 2)², where a and b are constants. a) Find the equations of motion for the system. b) Calculate and identify the conserved quantities. Is this system integrable? c) Calculate the energy function for the system.
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Transcribed Image Text:Consider a system with the following Lagrangian:
L = a(z² sin²
² sin² y + y²) + b(i cos y + 2)²,
y —
where a and b are constants.
a) Find the equations of motion for the system.
b) Calculate and identify the conserved quantities. Is this system integrable?
c) Calculate the energy function for the system..
1
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