Fractional Euler-Lagrange Equations Applied to Oscillatory Systems
نویسندگان
چکیده
منابع مشابه
The Euler – Lagrange Equations for Nonholonomic Systems
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conse...
متن کاملGeneralized Euler–Lagrange equations for fuzzy fractional variational calculus
This paper presents the necessary optimality conditions of Euler–Lagrange type for variational problems with natural boundary conditions and problems with holonomic constraints where the fuzzy fractional derivative is described in the combined Caputo sense. The new results are illustrated by computing the extremals of two fuzzy variational problems. AMS subject classifications: 65D10, 92C45
متن کاملEuler-lagrange Equations
. Consider a mechanical system consisting of N particles in R subject to some forces. Let xi ∈ R denote the position vector of the ith particle. Then all possible positions of the system are described by N -tuples (x1, . . . , xN ) ∈ (R) . The space (R) is an example of a configuration space. The time evolution of the system is described by a curve (x1(t), . . . , xN (t)) in (R) and is governed...
متن کاملThe Reduced Euler-Lagrange Equations
Marsden and Scheurle [1993] studied Lagrangian reduction in the context of momentum map constraints—here meaning the reduction of the standard Euler-Lagrange system restricted to a level set of a momentum map. This provides a Lagrangian parallel to the reduction of symplectic manifolds. The present paper studies the Lagrangian parallel of Poisson reduction for Hamiltonian systems. For the reduc...
متن کاملOn fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2015
ISSN: 2227-7390
DOI: 10.3390/math3020258