Approximate symmetries of a mathematical model describing one-dimensional motion in a nonlinear medium with a small dissipation are studied. In a physical application, the approximate solution is calculated making use of the approximate generator of the first-order approximate symmetry.

An essentially nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are derived. An application to a physiological model by M.C. Mackey is treated in detail.

This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the diffusion process, and the affect of the transport of an inert chemical species on the deformation of the solid. We then present a robust computational framewor...

MPC (Model Predictive Control) techniques, with constraints, are applied to a nonlinear vehicle model for the development of an ACC (Adaptive Cruise Control) system for transitional manoeuvres. The dynamic model of the vehicle is developed in the continuous-time domain and captures the real dynamics of the sub-vehicle models for steady-state and transient operations. A parametric study for the ...

In this article, we derive Ricker’s [22, 23] type nonlinear boundary condition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the convergence uniformly of the singularly perturbe...

Machine tools are designed to reach a given performance level in term of precision and static and dynamic stiffness. In this article, we present methods of evaluating linear axis dynamics starting from the dimensioning stage (simple dynamic model) up to complex modelling taking in consideration the disturbance force (constant and variable cutting force) and the controller. Further consideration...

The paper reriel\"s the known consequences of diffusion theory for the mathematical modelling of shrinkage, including the si::e dependence of drying half-time, and the initial and final asymptotic shapes of the time cun'es of total moisture loss, to which shrinkage is proportional. The mathematical arguments are extended and presented with greater rigour and generality than before, taking the n...

In this article we first present a mathematical model which describes the nonlinear dynamics of tensegrity structures. For certain tensegrity structures a particular class of motions, coined symmetrical motions, is defined. The corresponding equations of motion are derived and the conditions under which symmetrical motions occur are established. Reconfiguration procedures through symmetrical mo...

The grasping control problem for a hyperredundant arm is studied. Frist, dynamic model of the arm is analyzed. The control problems are divided in the subproblems: the position control in a desired reaching area, the control of the arm around the object-load and the force control of grasping. The difficulties determined by the complexity of the non-linear integral-differential equations are avo...

This paper presents a new educational analysis tool for the hydraulic wind power transfer system, which is commonly used in industrial processes. This system is complex and nonlinear and has a lot of parameters. Thus, this tool provides to teach undergraduate and graduate students without experimental laboratory setup. The nonlinear mathematical model of the system is firstly presented. Then th...