Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses ...

Physics-based simulation of deformable objects is a valuable tool for creating realistic and plausible computer graphics. However, even the calculations involved for simple abstractions like mass-spring models are highly demanding, especially when real-time simulation is desired. This diploma thesis explores the possibility to use the powerful vector computation engine present in modern 3D grap...

This paper discusses the constructional problem for a class of spring-mass systems whose part particles are connected to the ground. The problem is converted to an inverse eigenvalue problem for Jacobi matrix. An inverse eigenvalue problem of determining the system from its some physical parameters and incomplete eigenpairs is solved. The necessary and sufficient condition for constructing the ...

(*) Manuscrit re,u Ie lor octobre 1960. (**) Douglas Aircraft Co., Inc., EI Segundo, California (U.S.A.). The first-named author is also Professor of Mathematics at Pepperdine College, Los Angeles. California. tial factors may be demonstrated. Later the students are shown how to apply the principles they have learned to more complex systems. The spring-mass system can be seen in Fig. 2. The upp...

There are many ways of synthesizing sound on a computer. The method that we consider, called a mass-spring system, synthesizes sound by simulating the vibrations of a network of interconnected masses, springs and dampers. Numerical methods are required to approximate the differential equation of a mass-spring system. The standard numerical method used in implementing mass-spring systems for use...

In this paper we propose a method to simulate muscle deformation in real-time, still aiming at satisfying visual results; that is, we are not attempting perfect simulation, but building a useful tool for interactive applications. Muscles are represented at 2 levels: the action lines and the muscle shape. The action line represents the force produced by a muscle on the bones, while the muscle sh...

The objective of this lecture is to review the basic building blocks of lumped parameter rotational mechanical systems and to build the foundations that will enable you to model more complex dynamic systems consisting of translation and rotational elements. Corresponding to the translational elements mass, spring and damper, are the rotational inertia, rotational spring and rotational damper, r...