In physics, Lagrangian mechanics is an alternate formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced...

relativistic Lagrangian mechanics is Lagrangian mechanics applied in the context of special relativity and general relativity. The relativistic Lagrangian can...

Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces...

Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used...

reformulation of the original problem, known as the Lagrangian function or Lagrangian. In the general case, the Lagrangian is defined as L ( x , λ ) ≡ f ( x ) + ⟨...

In classical mechanics, Routh's procedure or Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by...

case one may revert to Newtonian mechanics. Two dominant branches of analytical mechanics are Lagrangian mechanics (using generalized coordinates and...

of energy Lagrangian mechanics, another theoretical formalism, based on the principle of the least action Classical statistical mechanics generalizes...

Semisprays arise naturally as the extremal curves of action integrals in Lagrangian mechanics. Generalizing all these examples, any (possibly nonlinear) connection...

density Lagrangian mechanics, a formulation of classical mechanics Lagrangian (field theory), a formalism in classical field theory Lagrangian point, a...

derivation of (Eq. 1) Equation 1 can additionally be obtained through Lagrangian Mechanics. More specifically, using the Euler–Lagrange equations (or Lagrange's...

of Y → X. In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle...

T^{*}Q} ; these coordinates are called the canonical coordinates. In Lagrangian mechanics, a different set of coordinates are used, called the generalized...

T={\tfrac {1}{2}}mv^{2}} and potential V {\displaystyle V} parts of the Lagrangian L = T − V {\displaystyle L=T-V} in arbitrary generalized coordinates the...

Hamiltonian constraint Moment map Contact geometry Analysis of flows Nambu mechanics Action (physics) Lagrangian Euler–Lagrange equations Noether's theorem...

Functional derivative Functional integration Hamiltonian mechanics Lagrangian Lagrangian mechanics Measure (physics) Noether's theorem Path integral formulation...

to the conservation of angular momentum throughout the motion. In Lagrangian mechanics, angular momentum for rotation around a given axis, is the conjugate...

translational symmetry. Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate...

In mathematics, the inverse problem for Lagrangian mechanics is the problem of determining whether a given system of ordinary differential equations can...

leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics). These advances, made predominantly in...

Lagrangian Particle Tracking (LPT) is a method used in fluid mechanics to analyse flow behaviour by tracking the motion of individual particles. It provides...

}}} Incorporating Lagrangian mechanics and using the Euler–Lagrange equation, Christoffel symbols can be substituted into the Lagrangian to account for the...

In celestial mechanics, the Lagrange points (/ləˈɡrɑːndʒ/; also Lagrangian points or libration points) are points of equilibrium for small-mass objects...

concepts. One of these instances occurs in Lagrangian mechanics. Lagrangian mechanics formulates mechanics in terms of generalized coordinates {qk}, which...

Displacement field (mechanics) Equivalent latitude Generalized Lagrangian mean Trajectory (fluid mechanics) Liouville's theorem (Hamiltonian) Lagrangian particle...

variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the system and...

zero-thickness (infinitely thin) string behaviour, using the principles of Lagrangian mechanics. Just as the action for a free point particle is proportional to...

Hamiltonian and Lagrangian systems. The term "geometric mechanics" occasionally refers to 17th-century mechanics. As a modern subject, geometric mechanics has its...

work–energy principle eliminates the constraint forces underlies Lagrangian mechanics. This section focuses on the work–energy principle as it applies...

Broglie relation is not true in a crystal. Most often in Lagrangian mechanics, the Lagrangian L(q, dq/dt, t) is in configuration space, where q = (q1,...