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1. INTRODUCTION In the field of motion dynamics, there are generally two methods used, Kinematics and Kinetics. Kinematics is the study of motion, describing how a hierarchical skeletal structure move irrespective of the real world forces that may or may not have an effective impact on the motion gaits. Whereas, the study involving the effect of real world… (More)
In the present we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms convex polytope. Finally, we study analogue of Birkhoff's theorem for the class of doubly stochastic operators .
In this paper, a procedural model has been developed for synthesizing cyclic horse motion through trigonometric functions. The system has been developed and implemented using mathematical model derived from trigonometric cyclic equations, along with forward and inverse kinematics to produce absolute gait control over the locomotion of horse character. The… (More)
This paper proposed doubly stochastic quadratic operators (DSQOs) for a consensus problem in multi-agent systems. The proposed scheme uses new nonlinear class model of family of quadratic stochastic operators (QSOs) for convergence consensus. The nonlinear model of QSOs plays an important role for reaching consensus. The nonlinear protocols for DSQOs are… (More)
In present paper we introduce the notion of dissipative quadratic stochastic operator and cubic stochastic operator. We prove necessary conditions for dissipativity of quadratic stochastic operators. Besides, it is studied certain limit behavior of such operators. Finally we prove ergodic theorem for dissipative operators.