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Variational principles --- Dynamics --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations

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Nonlinear operators --- Variational principles --- Differential equations, Partial --- Opérateurs non linéaires --- Principes variationnels --- Equations aux dérivées partielles --- 51 --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Operators, Nonlinear --- Operator theory --- Partial differential equations --- Mathematics --- 51 Mathematics --- Opérateurs non linéaires --- Equations aux dérivées partielles

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Finite element method --- Mechanics, Applied --- Variational principles. --- Mathematics. --- 51-72 --- -Variational principles --- #KVIV:BB --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematics--?-72 --- Mathematics --- Finite element method. --- 51-72 Mathematics--?-72 --- Variational principles --- Mathématiques --- Mécanique --- Mechanics, Applied - Mathematics. --- Methode variationnelle

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The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.

Least action. --- Variational principles. --- Mechanics. --- Lagrange equations. --- Hamilton-Jacobi equations. --- Equations, Hamilton-Jacobi --- Equations, Jacobi-Hamilton --- Jacobi-Hamilton equations --- Calculus of variations --- Differential equations, Partial --- Hamiltonian systems --- Mechanics --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Extremum principles --- Minimal principles --- Variation principles --- Variational principles

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Mathematical physics --- Differential geometry. Global analysis --- Gauge fields (Physics) --- Variational principles --- Champs de jauge (Physique) --- Principes variationnels --- 514.8 --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- Geometric study of objects of mechanics and physics --- Variational principles. --- Gauge fields (Physics). --- 514.8 Geometric study of objects of mechanics and physics