## An Introduction to the Use of Generalized Coordinates in Mechanics and Physics |

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actual forces actual motion angle angular velocity Bertrand's Theorem calculus of variations called center of gravity components concealed body configuration conservative forces constant constraints coordinates q cyclic coordinates degrees of freedom differential equations dt dt effective forces electromotive force equal equations of motion Euler's example expressed in terms forming the Lagrangian geometrical equations given Hamilton's principle Hamiltonian equations Hamiltonian function hanging particle Hence homogeneous quadratic hypothetical motion ignored coordinates impressed forces initial motion integral kinetic energy Lagrangian equation Lagrangian expression liquid momenta momentum moving particle moving system moving under conservative number of degrees position potential energy problem of Art rectangular axes rectangular coordinates remaining coordinates rigid body containing second wire simple pendulum sin2 smooth horizontal solve sphere starts from rest string Suppose tions tractrix virtual wedge Whence zero