Fractional treatment: an accelerated mass-spring system
ROMANIAN REPORTS IN PHYSICS(2022)
摘要
The aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.
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关键词
Mass-spring system,Laplace transform,Fractional Lagrangian,Approximation method
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