Graph ›
Part II ›
Calculus of Variations
Calculus of Variations
foundations +2 more results +39 more equations +26 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) definition 16.11: Admissible class; functional 16.11 Admissible class… definition 16.12: The two norms; weak and strong neighbourhoods 16.12 The two norms; w… definition 16.13: Weak and strong extrema 16.13 Weak and strong… definition 16.15: Variation; the first variation 16.15 Variation; the f… definition 16.47: Holonomic and nonholonomic constraints 16.47 Holonomic and no… definition 16.53: Jacobi accessory equation; conjugate point 16.53 Jacobi accessory… definition 16.59: Weierstrass excess function 16.59 Weierstrass exce… definition 16.62: Field of extremals; slope function 16.62 Field of extrema… definition 16.67: The Dirichlet principle 16.67 The Dirichlet pr… definition 16.75: Rayleigh quotient 16.75 Rayleigh quotient definition 16.83: One-parameter transformation group; variational
symmetry 16.83 One-parameter tr… definition 16.96: Action; Hamilton's principle 16.96 Action; Hamilton… definition 16.99: Abbreviated action 16.99 Abbreviated acti… proposition 16.1: The curve of quickest descent is a cycloid 16.1 The curve of qui… proposition 16.4: The hanging chain is a catenary 16.4 The hanging chai… proposition 16.6: The isoperimetric extremal is a circle 16.6 The isoperimetri… proposition 16.8: The minimal-surface equation 16.8 The minimal-surf… proposition 16.9: The catenoid 16.9 The catenoid proposition 16.16: Stationarity is necessary 16.16 Stationarity is… proposition 16.17: The first variation of an integral functional 16.17 The first variat… lemma 16.18: Fundamental lemma 16.18 Fundamental lemma lemma 16.19: du Bois-Reymond 16.19 du Bois-Reymond lemma 16.20: Mixed form 16.20 Mixed form theorem 16.22: Euler–Lagrange 16.22 Euler–Lagrange corollary 16.23: du Bois-Reymond form 16.23 du Bois-Reymond… proposition 16.26: Covariance under change of dependent variable 16.26 Covariance under… equation 16.1: eq:calcvar-brachistochrone-time eq. (16.1) equation 16.3: eq:calcvar-catenary-energy eq. (16.3) equation 16.6: eq:calcvar-area-functional eq. (16.6) equation 16.7: eq:calcvar-minimal-surface eq. (16.7) equation 16.11: eq:calcvar-basic-functional eq. (16.11) equation 16.14: eq:calcvar-gateaux eq. (16.14) equation 16.15: eq:calcvar-first-variation eq. (16.15) equation 16.18: eq:calcvar-dbr-hyp eq. (16.18) equation 16.20: eq:calcvar-euler-lagrange eq. (16.20) equation 16.25: eq:calcvar-beltrami eq. (16.25) equation 16.30: eq:calcvar-euler-lagrange-system eq. (16.30) equation 16.31: eq:calcvar-field-functional eq. (16.31) equation 16.32: eq:calcvar-euler-lagrange-field eq. (16.32) The chain of Calculus of Variations: 39 of 106 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.