equation 16.20 eq:calcvar-euler-lagrange

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equation 16.20: eq:calcvar-euler-lagrange16.20corollary 16.23: du Bois-Reymond form16.23definition 16.53: Jacobi accessory equation; conjugate point16.53proposition 16.28: Cyclic coordinate16.28proposition 16.26: Covariance under change of dependent variable16.26theorem 16.29: Beltrami identity16.29theorem 16.63: Hilbert's invariant integral16.63theorem 16.32: Transversality16.32theorem 7.43: Fundamental theorem of calculus, II7.43corollary 16.33: Weierstrass–Erdmann corner conditions16.33proof : ch:14-calculus-of-variations@proof-12proofequation 16.45: eq:calcvar-second-variation16.45proposition 23.53: A caustic point is a conjugate point23.53theorem A.436: Strengthened Jacobi condition and conjugate pointsA.436theorem 16.55: Jacobi's necessary condition16.55corollary 16.88: Momentum and angular momentum16.88proof : ch:14-calculus-of-variations@proof-14proofproposition 7.31: Chain rule7.31proof : ch:14-calculus-of-variations@proof-13proofproposition 16.105: The optical invariant in a stratified medium16.105proposition 16.39: Ostrogradsky instability16.39proof : ch:14-calculus-of-variations@proof-15proofdefinition 16.62: Field of extremals; slope function16.62proposition 7.136: Properties of conservative fields7.136remark 23.8: The action as a function, not a functional23.8theorem 16.64: Weierstrass' sufficient condition16.64proof : ch:14-calculus-of-variations@proof-30prooftheorem 16.31: Natural boundary condition16.31proof : ch:14-calculus-of-variations@proof-17proof

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depends_on du Bois-Reymond form declared parts/02-mathematical-methods/14-calculus-of-variations.tex:685
depends_on Jacobi accessory equation; conjugate point declared parts/02-mathematical-methods/14-calculus-of-variations.tex:1600
depends_on Cyclic coordinate declared parts/02-mathematical-methods/14-calculus-of-variations.tex:802
depends_on Covariance under change of dependent variable declared parts/02-mathematical-methods/14-calculus-of-variations.tex:746
depends_on Beltrami identity declared parts/02-mathematical-methods/14-calculus-of-variations.tex:819
depends_on Hilbert's invariant integral declared parts/02-mathematical-methods/14-calculus-of-variations.tex:1881
depends_on Transversality declared parts/02-mathematical-methods/14-calculus-of-variations.tex:891