The cauchy problem for mechanical systems with a finite number of degrees of freedom as a problem of continuation on the best parameter

1994 ◽  
Vol 58 (6) ◽  
pp. 955-962 ◽  
Author(s):  
Ye.B. Kuznetsov ◽  
V.I. Shalashilin
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
The Cauchy Problem ◽  
Best Parameter

scholarly journals The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms

2019 ◽  
Vol 21 (3) ◽  
pp. 317-328
Author(s):  
Marina V. Dontsova
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Local Solution ◽  
Quasilinear Equations ◽  
Solvability Conditions ◽  
First Order ◽  
The Cauchy Problem ◽  
Global Estimates

The Cauchy problem for a system of two first-order quasilinear equations with absolute terms is considered. The study of this problem’s solvability in original coordinates is based on the method of an additional argument. The existence of the local solution of the problem with smoothness which is not lower than the smoothness of the initial conditions, is proved. Sufficient conditions of existence are determined for the nonlocal solution that is continued by a finite number of steps from the local solution. The proof of the nonlocal resolvability of the Cauchy problem relies on original global estimates.

scholarly journals Vibration Protection of Mechanical Systems Consisting of Solid And Deformable Bodies

2018 ◽  
Vol 3 (9) ◽  
pp. 18
Author(s):  
Ismail Ibrahimovich Safarov ◽  
Teshaev Muhsin Khudoyberdiyevich
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Numerical Results ◽  
Constructive Method ◽  
Vibration Protection ◽  
Deformable Bodies ◽  
Reaction Forces ◽  
Active Vibration ◽  
Servo Constraints

In this  paper active vibration protection of mechanical systems consisting of solid and deformable bodies is considered. To actively control the oscillations of dissipative mechanical systems, a constructive method is used to determine the structure of the reaction forces of servo constraints. As an example, we consider the system with a finite number of degrees of freedom. Numerical results for various harmonic are also given.

Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms

2020 ◽  
Vol 55 ◽  
pp. 60-78
Author(s):  
M.V. Dontsova
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Local Solution ◽  
Quasilinear Equations ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
The Cauchy Problem ◽  
Global Estimates

We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms in the original coordinates is based on the method of an additional argument. Theorems on the local and nonlocal existence and uniqueness of solutions to the Cauchy problem are formulated and proved. We prove the existence and uniqueness of the local solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms, which has the same smoothness with respect to $x$ as the initial functions of the Cauchy problem. Sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms are found; this solution is continued by a finite number of steps from the local solution. The proof of the nonlocal solvability of the Cauchy problem for a system of two quasilinear equations of the first order with constant terms relies on global estimates.

Hamiltonian formulation for mechanical systems with nonholonomic constraints

2014 ◽  
Vol 11 (03) ◽  
pp. 1450017
Author(s):  
G. F. Torres del Castillo ◽  
O. Sosa-Rodríguez
Keyword(s):  
Finite Number ◽  
Mechanical System ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Hamiltonian Structure ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Hamilton Equations

It is shown that for a mechanical system with a finite number of degrees of freedom, subject to nonholonomic constraints, there exists an infinite number of Hamiltonians and symplectic structures such that the equations of motion can be written as the Hamilton equations, with the original constraints incorporated in the Hamiltonian structure.

scholarly journals A Method to Determine Structural Patterns of Mechanical Systems with Impacts

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Barbara Blazejczyk-Okolewska ◽  
Wioleta Serweta
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Matrix Representation ◽  
Mechanical Systems ◽  
Structural Classification ◽  
Structural Patterns ◽  
Equivalent Systems ◽  
Vibroimpact Systems

A structural classification of vibroimpact systems based on the principles given by Blazejczyk-Okolewska et al. (2004) has been proposed for an arbitrary finite number of degrees-of-freedom. A new matrix representation to formulate the notation of the relations occurring in the system has been introduced. The developed identification and elimination procedures of equivalent systems and identification procedures of connected systems enable the determination of a set of structural patterns of systems with impacts.

CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS

2005 ◽  
Vol 15 (01) ◽  
pp. 53-93 ◽  
Author(s):  
LAETITIA PAOLI
Keyword(s):  
Finite Number ◽  
Differential Inclusion ◽  
Continuous Dependence ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Approximate Solutions ◽  
Unilateral Constraints ◽  
Impact Problems ◽  
Continuous Dependence On Data ◽  
Continuous Dependence Of Solutions

We consider vibro-impact problems, i.e. mechanical systems with a finite number of degrees of freedom subject to frictionless unilateral constraints. The dynamics is described by a second-order measure differential inclusion completed by an impact law of Newton's type. Motivated by the computation of approximate solutions, we study in this paper the continuous dependence of solutions on data. When several constraints can be active at the same time, continuity on data does not hold in general and an example of such a behavior is presented. We then propose a criterion involving the geometry of the active constraints along the limit trajectory which ensures continuity on data.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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