Principles of DynamicsAn exploration of the principles of dynamics. |
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acceleration angle angular momentum angular velocity Assuming axis of symmetry calculate Cartesian center of mass circular coefficient components conservative constant constraint forces coordinate system corresponding cos² degrees of freedom differential equations direction disk ellipsoid equal equations of motion equilibrium Euler angles evaluated example expression external forces Əqi Figure fixed point force F forces acting friction function given in Eq Hence horizontal impulse inertia ellipsoid initial conditions integral kinetic energy Lagrange's equation law of motion let us consider linear momentum m₁ m₂ magnitude matrix mode moments of inertia moves Newton's law obtain orbit orthogonal particle of mass plane potential energy principal axes radius reference frame reference point relative result rigid body rotational motion scalar seen shown in Fig sin² sliding solve sphere transient solution unit vectors vertical virtual displacement x₁ xyz system zero