H. K. Kesavan

The vector-network model: A new approach to vector dynamics

Abstract This paper describes a procedure for applying graph theory to the analysis of general, dynamic, three-dimensional, lumped mechanical systems. The authors have observed the similarity between terminal graphs and three-dimensional vectors and have used it to develop the “vector-network model” which forms the bridge between vector methods and graph techniques. Previous applications of graph theory to scalar (one-dimensional) mechanical systems are seen to be a special case of vector-network model. The paper describes the construction and validity of the model, its use in formulating equations of motion and a prototype “self-formulating” computer program for dynamic simulation, based on the model.

The generalized maximum entropy principle

Generalizations of the maximum entropy principle (MEP) of E.T. Jaynes (1957) and the minimum discrimination information principle (MDIP) of S. Kullback (1959) are described. The generalizations have been achieved by enunciating the entropy maximization postulate and examining its consequences. The inverse principles which are inherent in the MEP and MDIP are made quite explicit. Several examples are given to illustrate the power and scope of the generalized maximum entropy principle that follows from the entropy maximization postulate. >

The MinMax information measure

The importance of finding minimum entropy probability distributions and the value of minimum entropy for a probabilistic system is discussed. A method to calculate these when there are both moment and inequality constraints on probabilities is given and illustrated with examples. It is shown that: information given by moments or inequalities on probabilities can be measured by the reduction in the uncertainty gap (S max - S min); and in certain circumstances the inequalities on probabilities can provide significant information about probabilistic systems.

Constrained multibody systems: graph-theoretic Newton-Euler formulation

With the aid of graph theory it is possible to combine the topological information of a constrained rigid-body system with the mathematical formulation of the equations of motion in a direct, systematic, and consistent procedural fashion that lends itself to a straightforward computer implementation. Such a graph-theoretical formulation for the dynamics analysis and simulation of three-dimensional constrained rigid-body systems is presented. It is shown that through the graph-theoretic approach, the topological information contributes directly to the systematic formulation procedure and also to an efficient, directly implementable computer algorithm. This algorithm can be implemented in a recursive fashion that reduces the computational cost substantially. The main components of the numerical procedure can be traced back directly to the system graphs of the formulation phase with very little effort. The resulting system of differential equations is left in its implicit form and solved numerically. >

A Systems Approach to Three-Dimensional Multibody Systems Using Graph-Theoretic Models

The discipline of linear graph theory, which has been applied extensively to the analysis of electrical networks, is now extended to encompass general three-dimensional isolated rigid-body systems. The graph-theoretic models of a rigid body and its relevant components are discussed elaborately to pave the way for further studies in multibody systems. Utilizing the analysis based on system topology, the mathematical model of a mechanical system is derived by means of a hybrid formulation in which Euler parameters (or normalized quaternions) are incorporated to define the orientations of rigid bodies. A single body system serves as an illustrative example.

Dynamics of 3-D isolated rigid-body systems: graph-theoretic models

Abstract The Graph-Theoretic Model (GTM) of a rigid body in three-dimensional space is presented for the study of multi-body systems. Euler parameters which represent normalized quaternions are introduced to specify the angular orientations of rigid bodies. A new type of formulation called Hybrid Formulation is designed to derive the mathematical model of an isolated rigid-body system. A two-body mechanical system serves as an illustrative example.

Piecewise Solution of the Load-Flow Problem

This paper presents the impedance and admittance forms of diakoptic solution of the load-flow problem on the basis of graph- theoretic concepts. The formulation does not assume a fixed slack bus voltage but instead takes into account the equation for total transmission line losses as an integral part of the scheme. Finally, test data based on this alternative formulation are presented for purposes of comparison With existing methods.

Graph-theoretic modeling of particle-mass and constrained rigid body systems☆

We show that the judicious combination of forces and torques in the construction of the balance of dynamical effects and the angular and the linear velocities for the imposition of kinematic constraints produces the desired general equations of motion in a simple and elegant manner

Graph-theoretic models for simulating robot manipulators

The graph-theoretic models of a prismatic joint, a revolute joint, and an open kinematic chain are presented. The Denavit-Hartenberg representation of linkages is encompassed within the general framework of graph-theoretic system theory. The final mathematical model derived by this formalism is a system of differential and algebraic equations.

Multi-body systems with open chains: Graph-theoretic models

Abstract On the basis of a hybrid formulation which was developed earlier for the graph-theoretic analysis of an isolated rigid-body system, this paper presents a model for a multi-body system with open kinematic chains. A new method for modelling a joint is presented, although the present discussion is restricted to the study of spherical joints. The manner in which the generalized coordinates for translation are chosen is governed by purely topological considerations whereas the choice of rotational coordinates is guided by the properties of Euler parameters which are normalized quaternions. A spinning top serves as an illustrative example.