A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters

Arsalan D. Mizhidon; Arsalan D. Mizhidon

doi:10.3934/math.2019.3.751

AIMS Mathematics

2019, Volume 4, Issue 3: 751-762. doi: 10.3934/math.2019.3.751

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A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters

Arsalan D. Mizhidon ^{1,2
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1.
Chair of Applied Mathematics, East Siberian State University of Technology and Management, Ulan-Ude, 670013, Russia
2.
Institute of Mathematics and Computer Science, Department of Applied Mathematics and differential equations, Buryat State University, Ulan-Ude, 670000, Russia

Received: 01 March 2019 Accepted: 11 June 2019 Published: 01 July 2019

A hybrid system of differential equations, which represents a generalized mathematical model for a system of rigid bodies mounted on an Euler-Bernoulli beam with the aid of springs, is described in the general form. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. Hybrid systems of differential equations of such type are normally constructed in the process of inference of dynamic equations for a given class of mechanical systems with the use of the Hamiltonian variation principle. The paper considers the analytical-numerical method proposed by the author, which is based on the mathematical apparatus of generalized functions. The comparative analysis of results of numerical computations obtained by the authoros method to the computational results obtained by the techniques known from the literature has shown the plausibility and universality of the authoros approach.
- mechanical systems,
- system of rigid bodies,
- generalized mathematical model,
- Euler-Bernoulli beam,
- hybrid systems of differential equations,
- Hamiltonian variation principle
Citation: Arsalan D. Mizhidon. A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters[J]. AIMS Mathematics, 2019, 4(3): 751-762. doi: 10.3934/math.2019.3.751

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Abstract

A hybrid system of differential equations, which represents a generalized mathematical model for a system of rigid bodies mounted on an Euler-Bernoulli beam with the aid of springs, is described in the general form. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. Hybrid systems of differential equations of such type are normally constructed in the process of inference of dynamic equations for a given class of mechanical systems with the use of the Hamiltonian variation principle. The paper considers the analytical-numerical method proposed by the author, which is based on the mathematical apparatus of generalized functions. The comparative analysis of results of numerical computations obtained by the authoros method to the computational results obtained by the techniques known from the literature has shown the plausibility and universality of the authoros approach.

References

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