Mechanical oscillators described by a system of differential-algebraic equations

Pražák, Dalibor, and Rajagopal, Kumbakonam R.. "Mechanical oscillators described by a system of differential-algebraic equations." Applications of Mathematics 57.2 (2012): 129-142. <http://eudml.org/doc/246446>.

@article{Pražák2012,
abstract = {The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide expressions for the forces in terms of kinematical quantities for the individual constituents. This is not possible for a very large class of problems where one can only provide implicit relations between the forces and the kinematical quantities. In certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force, which then reduces the problem to a system of differential-algebraic equations. We study such a system of differential-algebraic equations, describing the motions of the mass-spring-dashpot oscillator. Assuming a monotone relationship between the displacement, velocity and the respective forces, we prove global existence and uniqueness of solutions. We also analyze the behavior of some simple particular models.},
author = {Pražák, Dalibor, Rajagopal, Kumbakonam R.},
journal = {Applications of Mathematics},
keywords = {differential-algebraic equations; existence and uniqueness of solutions; mechanical oscillators; differential-algebraic equation; existence of solution; uniqueness of solution; mechanical oscillator},
language = {eng},
number = {2},
pages = {129-142},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mechanical oscillators described by a system of differential-algebraic equations},
url = {http://eudml.org/doc/246446},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Pražák, Dalibor
AU - Rajagopal, Kumbakonam R.
TI - Mechanical oscillators described by a system of differential-algebraic equations
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 129
EP - 142
AB - The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide expressions for the forces in terms of kinematical quantities for the individual constituents. This is not possible for a very large class of problems where one can only provide implicit relations between the forces and the kinematical quantities. In certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force, which then reduces the problem to a system of differential-algebraic equations. We study such a system of differential-algebraic equations, describing the motions of the mass-spring-dashpot oscillator. Assuming a monotone relationship between the displacement, velocity and the respective forces, we prove global existence and uniqueness of solutions. We also analyze the behavior of some simple particular models.
LA - eng
KW - differential-algebraic equations; existence and uniqueness of solutions; mechanical oscillators; differential-algebraic equation; existence of solution; uniqueness of solution; mechanical oscillator
UR - http://eudml.org/doc/246446
ER -