query: Why is the Lagrangian defined as $L=T - V$?
positive_passages.docid: 18054
positive_passages.text: Is there a proof from the first principle that the Lagrangian L = T - V?
negative_passages.docid: 125142
negative_passages.text: Example where Hamiltonian $H \neq T+V=E$, but $E=T+V$ is conserved
negative_passages.docid: 98800
negative_passages.text: Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$?
negative_passages.docid: 13644
negative_passages.text: Is the change in the Lagrangian always a total derivative for symmetry transformations of the action?
negative_passages.docid: 42186
negative_passages.text: When is the Hamiltonian of a system not equal to its total energy?
negative_passages.docid: 64727
negative_passages.text: Total time derivatives and partial coordinate derivatives in classical mechanics
negative_passages.docid: 99312
negative_passages.text: Why Lagrangian is negative number for a relativistic massive point particle?
negative_passages.docid: 70880
negative_passages.text: Invariance of canonical Hamiltonian equation when adding the total time derivative of a function of $q_i$ and $t$ to the Lagrangian
negative_passages.docid: 154454
negative_passages.text: Why are $L_4$ and $L_5$ lagrangian points stable?
negative_passages.docid: 90325
negative_passages.text: Why use the derivative and not the symmetric derivative?
negative_passages.docid: 41407
negative_passages.text: How to derive or justify the expressions of momentum operator and energy operator?
negative_passages.docid: 119380
negative_passages.text: Clarifying question on meaning of derivative of a linear transformation
negative_passages.docid: 35509
negative_passages.text: Noether's Theorem: Lie groups vs. Lie algebras; finite vs. infinitesimal symmetries
negative_passages.docid: 40355
negative_passages.text: Equivalence between Hamiltonian and Lagrangian Mechanics
negative_passages.docid: 91314
negative_passages.text: Advantages of Lagrangian Mechanics over Newtonian Mechanics
negative_passages.docid: 126142
negative_passages.text: Action principle, Lagrangian mechanics, Hamiltonian mechanics, and conservation laws when assuming Aristotelian mechanics $F=mv$
negative_passages.docid: 34788
negative_passages.text: Lagrangian for relativistic massless point particle