Inertial stabilization of a sensor mounted on nonstationary platforms is an important task in many applications such as image processing, astronomical telescopes, and tracking systems. For this purpose, some type of gimbaling arrangements is typically used. For implementing the LOS stabilization, usually a two-axes gimbal system is used which the sensor is mounted in the inner gimbal. The dynamic modeling and designing the control system for two axes gimbal system have been studied extensively, but there is a few works on three axes gimbal system. In this paper, the equation of motion for a three axes gimbal system is derived by the moment equation. The effect of angular velocities of the base into the gimbaled dynamic system and cross-coupling between gimbals are presented. In addition, some critical notes are presented for constructing the gimbal assembly. Moreover, a model based control strategy is proposed for controlling the gimbal dynamics.

It is well known that the solution of fractional models proved to be a powerful tool in studying various problems which appear in the sciences of real life. In view of the fact that economic applications are accelerating at an amazing pace, and the large number of modeling in this speciality, it has expanded the number of problems. So, our contribution is based on finding generalized solutions of a fractional differential equation known for their applications in microeconomics and finance and creating an algorithm which allows us to estimate the coefficients of this type of equation. And to really illustrate our results we will choose a model known in the stochastic literature by COGARCH but with fractional derivative, to demonstrate the asymptotic behavior of the estimators, including the impact of fractional order on the space of stochastic differential equations.

The paper develops the methods for computer simulation of the dynamics of absolutely rigid body systems with a tree structure. The equations of motion are presented in compact matrix form. The case of holonomic constraints is also considered. Since the independent parameters uniquely determine the positions and velocities of the bodies of the system in space, the generalized coordinates and variables with the dimension of impulses are chosen. A feature of the system of equations is that it is resolved with respect to the derivatives of the generalized momenta and does not contain constraint reactions. The derivation of the proposed form of the equations of motion from the Hamilton principle using the matrix-geometric approach is given. Recursive formulas for determining all kinematic and dynamic variables included in the equations are obtained. As an example of a mechanical system with six degrees of freedom, all stages of preparing primary information and compiling equations of motion in the proposed form are demonstrated. Three algorithms are presented that allow resolving the obtained extended system of equations with respect to the generalized velocities and momenta without direct formation of the Hamilton equations. The classification of the equations of motion of rigid body systems is carried out from their structure point of view. The place of the deduced equations in the general classification is also demonstrated. A comparative analysis of the computational complexity of the considered methods for various classes of mechanical systems is carried out. Some diagrams are constructed that allow choosing the most effective modeling method depending on the characteristics of the mechanical system: the number of bodies, the number of degrees of freedom and the structure of the system.

Here, the existence and measurability of solutions for stochastic differential equations driven by fractional Brownian noise with Hurst parameter greater than 1/2 is proved. Our method is based on approximating the main equation by delayed equations as in Peano’s method in ODEs. This method makes the proofs easier and needs weaker assumptions for the existence part, compared with the previous works as in [25]. In addition the constructive nature of the proofs helps to develop some numerical methods for solving such SDEs.