Extended Lagrange

Differential calculus in one variable: theory and applications for optimisation, approximations, and plotting functions

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to the English translation of Lagrange's Mecanique Analytique Lagrange's Mecanique Analytique appeared early in 1788 almost exactly one cen­ tury after the publication of Newton's Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet­ ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au­ thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and methods to investigate problems in constrained interaction, fluid flow, elasticity, strength of materials and the operation of machines. The Mecanique Analytique was a remarkable work of compilation that became a fundamental reference for subsequent research in exact science.

to the English translation of Lagrange's Mecanique Analytique Lagrange's Mecanique Analytique appeared early in 1788 almost exactly one cen­ tury after the publication of Newton's Principia Mathematica. It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet­ ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au­ thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and methods to investigate problems in constrained interaction, fluid flow, elasticity, strength of materials and the operation of machines. The Mecanique Analytique was a remarkable work of compilation that became a fundamental reference for subsequent research in exact science.

This volume provides a short summary of the essentials of Lagrangian dynamics for practicing engineers and students of physics and engineering. It examines a range of phenomena and techniques in a style that is compact and succinct, while remaining comprehensive.