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- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/28%3A_Eulers_Equations/28.02%3A_Free_Rotation_of_a_Symmetric_Top_Using_Eulers_EquationsThis is a problem we’ve already solved, using Lagrangian methods and Euler angles, but it’s worth seeing just how easy it is using Euler’s equations.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/04%3A_Rigid_Body_Rotation/4.05%3A_Euler's_Equations_of_MotionEuler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with its axes fixed to the b...Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with its axes fixed to the body and parallel to the body's principal axes of inertia.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/28%3A_Eulers_Equations/28.01%3A_Introduction_to_Eulers_EquationsWe’ve just seen that by specifying the rotational direction and the angular phase of a rotating body using Euler’s angles, we can write the Lagrangian in terms of those angles and their derivatives, a...We’ve just seen that by specifying the rotational direction and the angular phase of a rotating body using Euler’s angles, we can write the Lagrangian in terms of those angles and their derivatives, and then derive equations of motion. These can be solved to describe precession, nutation, etc.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/05%3A_Calculus_of_Variations/5.03%3A_Applications_of_Eulers_EquationThe Brachistochrone problem involves finding the path having the minimum transit time between two points. The Brachistochrone problem stimulated the development of the calculus of variations by John B...The Brachistochrone problem involves finding the path having the minimum transit time between two points. The Brachistochrone problem stimulated the development of the calculus of variations by John Bernoulli and Euler.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/28%3A_Eulers_EquationsThumbnail: Classic Euler angles geometrical definition. The xyz (fixed) system is shown in blue, the XYZ (rotated) system is shown in red. The line of nodes (N) is shown in green (CC BY-SA 3.0; Lionel...Thumbnail: Classic Euler angles geometrical definition. The xyz (fixed) system is shown in blue, the XYZ (rotated) system is shown in red. The line of nodes (N) is shown in green (CC BY-SA 3.0; Lionel Brits via Wikipedia)
