Derivation of First-Order Difference Equations for Dynamical Systems by Direct Application of Hamilton’s Principle

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Abstract
In dynamics problems where the equations of motion are eventually reduced to finite-difference equations for numerical integration on a digital computer, an auxiliary condition exists that permits the application of the Lagrangian multiplier method to Hamilton’s principle in order to obtain directly a set of first-order difference equations. These equations are equivalent to Hamilton’s canonical equations and are derived without the necessity to obtain the Hamiltonian or take time derivatives.

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