A new form of equations for rigid body rotational dynamics

U ovom je radu izveden novi oblik diferencijalnih jednadžbi koje opisuju dinamiku rotacijskog gibanja krutog (čvrstog) tijela oko središta njegove mase. Kao varijable koriste se tri s-parametra (modificirani parametri Rodriga-Hamiltona) i tri parametra kutne brzine tijela. Izvedene jednadžbe su osobito korisne za analitičko i numeričko izučavanje rotacijskog gibanja čvrstog tijela. Istražena je topološka struktura konfiguracijskog s-prostranstva za uravnoteženo kruto tijelo. Razmotren je primjer uporabe izvedenih jednadžbi koje opisuju rotacijsko gibanje krutog tijela u otpornoj sredini.In the paper, a new form of differential equations for rigid body attitude dynamics is obtained. Three s-parameters (modified Rodrigues-Hamilton parameters) and three angular velocity parameters are used as unknown variables. Built equations are particularly useful for analytical and numerical study of rotational motion of a rigid body. The topological structure of configurational s-manifold for a balanced rigid body is investigated. An example of the use of constructed equations to describe the rotational motion of a rigid body in a resisting medium is considered

A new form of equations for rigid body rotational dynamics

In the paper, a new form of differential equations for rigid body attitude dynamics is obtained. Three s-parameters (modified Rodrigues-Hamilton parameters) and three angular velocity parameters are used as unknown variables. Built equations are particularly useful for analytical and numerical study of rotational motion of a rigid body. The topological structure of configurational s-manifold for a balanced rigid body is investigated. An example of the use of constructed equations to describe the rotational motion of a rigid body in a resisting medium is considered

Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions

Here, we study the internal variable approach to viscoelasticity. First, we generalize the classical approach by introducing a fractional derivative into the equation for time evolution of the internal variables. Next, we derive restrictions on the coefficients that follow from the dissipation inequality (entropy inequality under isothermal conditions). In the example of wave propagation, we show that the restrictions that follow from entropy inequality are sufficient to guarantee the existence of the solution. We present a numerical solution to the wave equation for several values of the parameters

Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions

Here, we study the internal variable approach to viscoelasticity. First, we generalize the classical approach by introducing a fractional derivative into the equation for time evolution of the internal variables. Next, we derive restrictions on the coefficients that follow from the dissipation inequality (entropy inequality under isothermal conditions). In the example of wave propagation, we show that the restrictions that follow from entropy inequality are sufficient to guarantee the existence of the solution. We present a numerical solution to the wave equation for several values of the parameters

Optimal Shape and First Integrals for Inverted Compressed Column

We study optimal shape of an inverted elastic column with concentrated force at the end and in the gravitational field. We generalize earlier results on this problem in two directions. First we prove a theorem on the bifurcation of nonlinear equilibrium equations for arbitrary cross-section column. Secondly we determine the cross-sectional area for the compressed column in the optimal way. Variational principle is constructed for the equations determining the optimal shape and two new first integrals are constructed that are used to check numerical integration. Next, we apply the Noether’s theorem and determine transformation groups that leave variational principle Gauge invariant. The classical Lagrange problem follows as a special case. Several numerical examples are presented

Preisach Elasto-Plastic Model for Mild Steel Hysteretic Behavior-Experimental and Theoretical Considerations

The Preisach model already successfully implemented for axial and bending cyclic loading is applied for modeling of the plateau problem for mild steel. It is shown that after the first cycle plateau disappears an extension of the existing Preisach model is needed. Heat dissipation and locked-in energy is calculated due to plastic deformation using the Preisach model. Theoretical results are verified by experiments performed on mild steel S275. The comparison of theoretical and experimental results is evident, showing the capability of the Presicah model in predicting behavior of structures under cyclic loading in the elastoplastic region. The purpose of this paper is to establish a theoretical background for embedded sensors like regenerated fiber Bragg gratings (RFBG) for measurement of strains and temperature in real structures. In addition, the present paper brings a theoretical base for application of nested split-ring resonator (NSRR) probes in measurements of plastic strain in real structures

A New Model of the Fractional Order Dynamics of the Planetary Gears

A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained

A note on the paper: "Nonlinear integral equations with new admissibility types in b-metric spaces"

In this paper we consider, discuss and slightly complement recent fixed point results for mappings in b-metric spaces established by Sintunavarat (J Fixed Point Theory Appl 18:397-416, 2016). Thus, all our results are with shorter proofs. In addition, an application to integral equations is given to illustrate the usability of our approach