This work relates to the field of thermophysical parameters of refractory interstitial alloys. The isochoric heat capacity of cubic titanium carbide TiCx has been calculated within the Debye approximation in the carbon concentration  range x = 0.70–0.97 at room temperature (300 K) and at liquid nitrogen temperature (80 K) through the Debye temperature established on the basis of neutron diffraction analysis data. It has been found out that at room temperature with decrease of carbon concentration the heat capacity significantly increases from 29.40 J/mol·K to 34.20 J/mol·K, and at T = 80 K – from 3.08 J/mol·K to 8.20 J/mol·K. The work analyzes the literature data and gives the results of the evaluation of the high-temperature dependence of the heat capacity СV of the cubic titanium carbide TiC0.97 based on the data of neutron structural analysis. It has been proposed to amend in the Neumann–Kopp formula to describe the high-temperature dependence of the titanium carbide heat capacity. After the amendment, the Neumann–Kopp formula describes the results of well-known experiments on the high-temperature dependence of the heat capacity of the titanium carbide TiCx. The proposed formula takes into account the degree of thermal excitation (a quantized number) that increases in steps with increasing temperature.The results allow us to predict the thermodynamic characteristics of titanium carbide in the temperature range of 300–3000 K and can be useful for materials scientists.

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where D w -matrix of the variable coefficients constraints equations according program trajectories w(t) , wet) -second (2) (1){~~-D~P = f(i, x,t) + u(t), (x,x) accomplish stability analysis of nonlinear equation of motion at large neighborhood of current position.The main advantage of walking machines is the possibility of walking on various kind of surface. There are some examples of solving control problem via multibody dynamics methods at automotive, where the control defines via feedback constants. At robotics original methods for define multidimensional control function at mechanical systems prescribed structure have been proposed [4]. Most common method for control movement synthesis is inverse dynamic method [3], [5]. Multibody dynamics method provides solution of control problem for mechanical system with arbitrary structure. In this work, we present a methodology that is suitable for spatial mechanical system with redundant constraints and drives, and provides a stable movement. II. EQUATIONS OF THE METHOD Programming realization of inverse dynamics method for synthesis of control movement of multidimensional walking robot based on differential algebraic equations. where x is state vector dimension n, M -inertia matrix, f'(x, x, t) -external forces vector, o(t) -control forces vector with dimension m , D -matrix of the variable coefficients constraints equations with dimension k x n, k -number of constraints equations, h(i, x) -right side constraints equations vector, p -Lagrange multipliers vector. Let control motion is the movement some prescribe point of the system along program trajectories wet) , wet) -vector with dimension I . Eq. (1) can be transforming by substitute control forces o(t) on constraints equation due program trajectories wet) :The problem of inverse dynamics control is considered in biomechanics and robotics. It is actually at robotics, medicine (limbs prosthetics) and new types of machines. The theory of control is based on fundamental idea of dynamic inverse. One of the best control schemes is hybrid position/force [1]. Ones works has been exploited the hybrid control to manipulators with open constraints. The theory of the control of robotics with closured constraints [2] assumed that the rectangular matrix of the coefficients of constraints is the matrix of full rank, and not include redundant constraints. The problem of the redundant constraints takes place at walking machines and systems with redundantly drive parallel mechanisms [3].The mentions methods are references at two classes of mechanical systems. First it is spatial system with unmovable body and seconds is a spatial system without unmovable body. The dynamics of the first class systems is described by equations, expressed in explicit form using relative or absolute coordinates. That form of equations is permitted simple using classical method of stability analysis. This method is wellsuitable for control and stability analysis of the manipulators with end effectors constrained, parallel manipulators and multifing...