What is the significance of quadrature in rigid body rotation?

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SUMMARY

The significance of quadrature in rigid body rotation is primarily related to the reduction of complex systems into manageable integrals. In this context, quadrature refers to expressing the solution as a one-dimensional integral, where the integrand is an explicit function of the integration variable. This method is crucial for deriving the Lagrangian and Hamiltonian formulations of motion in rigid body dynamics. Understanding quadrature allows for more straightforward computation of integrals necessary for analyzing physical systems.

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Rubyeye
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In rigid body rotation, there is some question.
First, problem give me Lagrangian.
And, I have to compute Hamiltonian.
Then, problem said that "Reduce the system to quadratures (i.e., write the solution in the form of a one dimensional integral whose integrand is an explicit function of the integration variable.) "

What does quadrature mean?
 
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