Dynamics of theN-link pendulum: a fractional perspective

Abstract

This paper addresses the dynamics of an N-link planar pendulum in the perspective of fractional calculus. The proposed methodology leads to a novel point of view for signal propagation as a timespace wave within the system mechanical structure. Numerical simulations show the effectiveness of the approach both for signal visualisation and limit cycle detection.

Geometric modeling of the unfolding of a rod structure in the form of a double spherical pendulum in weightlessness

“…In practical terms, this represents [6] the construction and solving the Lagrange equations of second kind for the motion of a mechanical system relative to the generalized coordinates. As well as studying the dynamics of a multilink pendulum, using, for example, the methods of fractional calculus [7]. However, the cited (and similar) papers did not pay enough attention to the graphical interpretation of the obtained solutions.…”

“…are the derivatives from the function of description of the generalized coordinates. Equations (7) in the expanded form are not given due to their cumbersome form. We employed the mathematical software package maple, able to operate with information in the form of analytical expressions.…”

Geometrical modeling of the unfolding of spatial rod structures, similar to the four-link pendulum, in weightlessness

“…Paper [7] reports a study into the dynamics of an N-link pendulum; article [8] -into simulation of oscillations of the pendulum whose elements are geometrical objects. However, papers [7,8] lack the graphical confirmation of the simulation result. Certain features of the mathematical processor maple to simulate the oscillations of a multi-link pendulum were demonstrated in work [9].…”

“…The result of a review of the scientific literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] is those issues that have not been yet studies by other authors, which allowed us to formulate the following research problem. There is a need to devise techniques:…”

“…To describe the motion of a four-link rod structure, it is necessary to construct and solve a system of the Lagrange equations of the second kind [7][8][9]. To this end, using the generalized coordinates, we calculate "virtual" coordinates of the nodal points:…”