Salles, Mário OtávioFaria, Yuri Medeiros de2020-02-132021-09-292020-02-132021-09-292019-12-13FARIA, Yuri Medeiros de. Condições de transversalidades na mecânica. 2019. 41f. Trabalho de Conclusão de Curso (Graduação em Física) - Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal, 2019.https://repositorio.ufrn.br/handle/123456789/40265In this work we show a deduction of Euler-Lagrange equation and transversality conditions in a geometric view. To do that we use a functional F, measuring some physical aspect of our system, as a function over the set of all possible solutions φ(t) = (t, q(t), q̇(t)) that describe the development of the system. To generate this set, given one curve φ(t), we compose it with two one-parameter groups of functions, φ{Q, Ɛ} at left and φ^{ −1}{I, Ɛ} at right, and after that generate a family of curves φƐ (t) = φ{Q, Ɛ} ◦ q ◦ φ^{−1}_(I, Ɛ} (t). The first composition generate vertical variations and the second one generate horizontal variations. To choose the solution φ(t) = (t, q(t), q̇(t)) that can be a candidate to optimal solution of our problem we use the variational principle F'[φ] = 0.cálculo variacionalvariational calculuscondições de transversalidadeequação de Eulertransversality conditionEuler equationbachelorThesis