Graph ›
Part III ›
Lagrangian Mechanics
Lagrangian Mechanics
foundations +9 more results +5 more equations +14 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) notation 21.1: not:lag-indices 21.1 notation definition 21.2: Holonomic constraint 21.2 Holonomic constr… definition 21.5: Non-holonomic constraint 21.5 Non-holonomic co… definition 21.9: Degrees of freedom 21.9 Degrees of freed… definition 21.12: Generalized coordinates 21.12 Generalized coor… definition 21.14: Constraint force 21.14 Constraint force definition 21.15: Active force 21.15 Active force definition 21.16: Compatible and invertible virtual displacements 21.16 Compatible and i… definition 21.17: Virtual work 21.17 Virtual work definition 21.19: Inertial force 21.19 Inertial force definition 21.29: Generalized force 21.29 Generalized force definition 21.31: Lagrangian 21.31 Lagrangian definition 21.34: Generalized momentum 21.34 Generalized mome… theorem 21.18: Principle of virtual work 21.18 Principle of vir… theorem 21.20: d'Alembert's principle 21.20 d'Alembert's pri… theorem 21.21: Lagrange equations of the first kind 21.21 Lagrange equatio… proposition 21.22: Determinacy of the first-kind system 21.22 Determinacy of t… proposition 21.25: Departure from a smooth sphere 21.25 Departure from a… theorem 21.30: Lagrange equations of the second kind 21.30 Lagrange equatio… theorem 21.32: Lagrange equations 21.32 Lagrange equatio… theorem 21.36: Conservation of the conjugate momentum 21.36 Conservation of… proposition 21.38: Energy in generalized coordinates 21.38 Energy in genera… proposition 21.41: Time derivative of the Jacobi integral 21.41 Time derivative… theorem 21.43: Conservation of energy 21.43 Conservation of… theorem 21.46: Hamilton's principle 21.46 Hamilton's princ… theorem 21.53: Equations of motion of a nonholonomic system 21.53 Equations of mot… equation 21.7: eq:lag-gct eq. (21.7) equation 21.12: eq:lag-constraint-hypothesis eq. (21.12) equation 21.17: eq:lag-pvw eq. (21.17) equation 21.19: eq:lag-dalembert eq. (21.19) equation 21.21: eq:lag-constraints-fk eq. (21.21) equation 21.22: eq:lag-first-kind eq. (21.22) equation 21.28: eq:lag-sphere-departure eq. (21.28) equation 21.31: eq:lag-generalized-force eq. (21.31) equation 21.32: eq:lag-second-kind eq. (21.32) equation 21.37: eq:lag-lagrangian eq. (21.37) equation 21.38: eq:lag-lagrange-equations eq. (21.38) equation 21.39: eq:lag-el-conservative eq. (21.39) equation 21.43: eq:lag-generalized-momentum eq. (21.43) The chain of Lagrangian Mechanics: 39 of 67 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.