The present paper is concerned with the calculation of the human hip joint parameters for periodic, stochastic unsteady, motion with asymmetric probability density function for gap height. The asymmetric density function indicates that the stochastic probabilities of gap height decreasing are different in comparison with the probabilities of the gap height increasing. The models of asymmetric density functions are considered on the grounds of experimental observations. Some methods are proposed for calculation of pressure distributions and load carrying capacities for unsteady stochastic conditions in a super thin layer of biological synovial fluid inside the slide biobearing gap limited by a spherical bone acetabulum. Numerical calculations are performed in Mathcad 12 Professional Program, by using the method of finite differences. This method assures stability of numerical solutions of partial differential equations and gives proper values of pressure and load carrying capacity forces occurring in human hip joints.
The paper deals with the H2-norm of finite dimensional linear continuous-time periodic (FDLCP) systems, represented in state space. on basis of general formulae for the H2-norm significantly simpler formulae are derived under the assumption of stability of the system. the proposed method needs to compute the transition matrix on the interval (...) An example is given, where the H2-norm is determined exactly, and the proposed method turns out to be superior to other known methods.
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This paper presents the author's numerical contribution to unsymmetrical viscoelastic hydrodynamic lubrication of human joints with synovial fluid in periodically changed time and unsteady magnetic field. We assume that bone head in human joint moves in two directions, namely in circumference and meridian directions. Basic equations describing the flow of synovial fluid in human hip joint are solved analytically od numerically. Numerical calculations are performed in Mathcad 2000 Professional Program, taking into account the method of finite differences. This method satisfies stability of numerical solutions of partial differential equations and values of capacity forces occurring in human joints.
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