Lagrangians Galore
arXiv:0706.1008 · doi:10.1063/1.2821612
Abstract
Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
16 pages
Cited by in corpus (20)
- A direct approach to the construction of standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients
- Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems
- Inverse variational problem for non-standard Lagrangians
- An old Method of Jacobi to find Lagrangians
- Special Functions of Mathematical Physics: A Unified Lagrangian Formalism
- An algebraic approach to laying a ghost to rest
- Using an old method of Jacobi to derive Lagrangians: a nonlinear dynamical system with variable coefficients
- Lagrangian formalism and Lie group approach for commutative semigroup of differential equations
- New non-standard Lagrangians for the Liénard-type equations
- From Lagrangian to Quantum Mechanics with Symmetries
- Gauge Functions in Classical Mechanics: From Undriven to Driven Dynamical Systems
- Nonstandard Null Lagrangians and gauge Functions for Newtonian Law of Inertia
- On the inverse problem of the discrete calculus of variations
- New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems
- General Null Lagrangians and Their Novel Role in Classical Dynamics
- Quantizing preserving Noether symmetries
- A New Fundamental Asymmetric Wave Equation and its Application to Acoustic Wave Propagation
- Quantization of nonlinear non-Hamiltonian systems
- Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries
- Null Lagrangians and Invariance of Action: Exact Gauge Functions