Ivan Kosenko

The motion of a spacecraft containing a moving massive point in the central field of Newtonian attraction is considered. Within the framework of the so-called “satellite approximation”, the center of mass of the system is assumed to move in an unperturbed elliptical Keplerian orbit. The spacecraft’s dynamics about its center of mass is studied. Conditions under which the spacecraft rotates about a perpendicular to the plane of the orbit uniformly with respect to the true anomaly are found. Such uniform rotations are achieved using a specially selected rule for changing the position of a massive point with respect to the spacecraft. Necessary conditions for these uniform rotations are studied numerically. An analysis of the nonintegrability of a special class of spacecraft’s rotation is carried out using the method of separatrix splitting. Poincaré sections are constructed for certain parameter values. Several linearly stable periodic motions are pointed out and investigated.

The problem of the motion of a particle in the gravity field of a homogeneous dumbbell-like body composed of a pair of intersecting balls, whose radii are, in general, different, is studied. Approximation for the Newtonian potential of attraction is obtained. Relative equilibria and their properties are studied under the assumption of uniform rotation of the dumbbells.

The omniwheel is defined as a wheel having rollers along its rim. Accordingly, the omnivehicle is a vehicle equipped with omniwheels. Several steps of development of the dynamical model of the omni vehicle multibody system are implemented. Initially, the dynamics of the free roller moving in a field of gravity and having a unilateral rigid contact constraint with a horizontal surface is modeled. It turned out that a simplified and efficient algorithm for contact tracking is possible. On the next stage the omniwheel model is implemented. After that the whole vehicle model is assembled as a container class having arrays of objects as instantiated classes/models of omniwheels and joints. The dynamical properties of the resulting model are illustrated via numerical experiments.

A dynamical model of the gearbox with spur involute mesh is under construction. The main attention is paid to the design technology of the cylindrical bodies elastic contact models. First of all, an algorithm for tracking of contact for cylindrical surfaces directed by involutes underwent upgrading. This algorithm is reduced «simply» to tracking of two involutes. As a result it turned out that common line normal to both curves, involutes, of contacting coincides always with line of action. This causes immediately a simplified technique for contact tracking without use of differential or algebraic equations. This technique is reduced to simple formulae for direct computations. At the same time dynamical models of the bodies involved, gearwheels and gearbox housing, continue to be three-dimensional.

Contact model provides a full possibility to take into account unilateral nature of teeth interacting while meshing. The backlash may arise dynamically for any side of teeth pairs at contact. In particular, the model simulates dynamics for arbitrary regimes of the pinion rotation acceleration/deceleration.

The mesh construct is such that for any side (for both the forward and backward contacting) of teeth at contact the mesh ratio is greater than one. The mesh multiplicity for real gears prevents potential jamming for gearwheels while the teeth pairs switching process. Thus our implementation assumes mesh cycles overlapping: new contact arises beforehand the old one will vanish.

In frame of the Hertz contact problem an approximate model to compute resulting wrench of the dry friction tangent forces is built up. The wrench consists of the total friction force and the drilling friction torque. An approach under consideration develops in a natural way the contact model built up earlier. The dry friction forces and torque are integrated over the contact elliptic spot. Generally an analytic computation of the integrals mentioned leads to the cumbersome calculation, decades of terms, including rational functions depending in turn on complete elliptic integrals. To implement the elastic bodies contact interaction computer model fast enough one builds up the approximate model in the direction as it was proposed by Contensou. The model under construction is one derived from the Contensou simplified model in the following directions: (a) the model is anisotropic: the total friction forces along ellipse axes are different; (b) for the translatory and almost translatory relative motions one uses the Coulomb friction law regularization; © the approximate model for the drilling torque also has been constructed. To verify the model built the results obtained by several authors were used. The Tippe-Top dynamic model is used as a an example under testing. It turned out the top revolution process is identical to one simulated using the set-valued functions approach. The ball bearing dynamic model is used to verify different approaches to the tangent forces computational implementation in details. The model objects corresponding to contacts between the balls and raceways were replaced by ones of new class developed here. Then the old friction model of the regularized Coulomb type and the new one, approximate Contensou, each embedded into the whole bearing dynamic model were thoroughly tested and compared. It turned out the simplified Contensou approach provides the computer model even faster in compare with the case of the point contact.