What is the significance of quadrature in rigid body rotation?

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Quadrature in the context of rigid body rotation refers to the process of reducing a complex system to a one-dimensional integral, allowing for easier computation of solutions. It involves expressing the solution in a form where the integrand is a function of the integration variable. The discussion highlights the need to compute the Lagrangian and Hamiltonian for the system before applying quadrature techniques. Understanding quadrature is essential for solving integrals that arise in the analysis of rigid body dynamics. This method simplifies the mathematical treatment of rotational motion in physics.
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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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