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Representations of the Motion
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angular velocity apsidal axis called Cartesian coordinates catastatic central force configuration space Consider const constant constraint equations constraint forces coordinate system curve d'Alembert's principle defined denote derivable differential direction disk dynamics energy integral equations of constraint equations of motion Euler angles Example exists finite force components forces acting formulation fundamental equation given forces gives gyroscope Hamilton's principle Hence holonomic constraints horizontal inertia infinitesimal initial conditions kinetic energy Lagrange multipliers Lagrange's equations Lagrangean mechanics Legendre transform Liapunov Liapunov function linear mass center massless matrix Newtonian nonholonomic constraints particle mechanics particle of mass pendulum Pfaffian Pfaffian form possible velocity potential energy problem quadratures quantity radius rigid body rotation satisfy scleronomic shown in Fig smooth solution stability substitution surface system of particles tangent plane theorem trajectory transformation unit vectors variables variation vertical virtual displacements write zero