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    • https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/13%3A_Lagrangian_Mechanics/13.02%3A_Generalized_Coordinates_and_Generalized_Forces
      A state of a molecule may described by a number of parameters, e.g., bond lengths and the angles). These bonds lengths and bond angles constitute a set of coordinates which describe the molecule. We a...A state of a molecule may described by a number of parameters, e.g., bond lengths and the angles). These bonds lengths and bond angles constitute a set of coordinates which describe the molecule. We are not going to think about any particular sort of coordinate system or set of coordinates. Rather, we are going to think about generalized coordinates, which may be lengths or angles or various combinations of them.
    • https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/06%3A_Lagrangian_Dynamics/6.05%3A_Constrained_Systems
      The motion for systems subject to constraints is difficult to calculate using Newtonian mechanics because all the unknown constraint forces must be included explicitly with the active forces in order ...The motion for systems subject to constraints is difficult to calculate using Newtonian mechanics because all the unknown constraint forces must be included explicitly with the active forces in order to determine the equations of motion. Lagrangian mechanics avoids these difficulties by allowing selection of independent generalized coordinates that incorporate the correlated motion induced by the constraint forces. This allows the constraint forces acting on the system to be ignored.
    • https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/04%3A_Rigid_Body_Rotation/4.04%3A_Lagrange's_Equations_of_Motion
      In deriving Euler’s equations, I find it convenient to make use of Lagrange’s equations of motion. This will cause no difficulty to anyone who is already familiar with Lagrangian mechanics. The geomet...In deriving Euler’s equations, I find it convenient to make use of Lagrange’s equations of motion. This will cause no difficulty to anyone who is already familiar with Lagrangian mechanics. The geometrical description of a mechanical system at some instant of time can be given by specifying a number of coordinates, e.g., if the system consists of just a single particle, you could specify its rectangular coordinates xyz or its cylindrical coordinates ρϕz , or its spherical coordinates rθϕ .
    • https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/06%3A_Lagrangian_Dynamics/6.03%3A_Lagrange_Equations_from_dAlemberts_Principle
      The Principle of Virtual Work provides a basis for a rigorous derivation of Lagrangian mechanics.

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