Experimental observation of stabilization of tippe top spinning on a vibrating plane
Alexander A. Kilin and Yury L. Karavaev
Available online 10 January 2025

Abstract
This paper presents an experimental study of the motion of a spherical body with a displaced center of mass on a surface undergoing oscillations in the vertical plane. The phenomenon of vibrostabilization of an unstable position in which the center of mass of the body is above the geometric center of the sphere is revealed. The influence of the frequency and amplitude of oscillations of the surface on the stabilization of the unstable position of the motion of the spherical body is analyzed.

Mathematics Subject Classification
74H45; 70-05, 70E50

Keywords
spherical top, vibrating plane, stabilization, experiment

DOI
https://doi.org/10.2298/TAM241204001K

Erratum to: Symmetries and stability of motions in the Newtonian and the Hookean potentials (Theor. Appl. Mech. 49(1) (2022), 61--69) DOI: https://doi.org/10.2298/TAM220213005C
Christian Carimalo
Available online 28 February 2025

Abstract

Mathematics Subject Classification

Keywords

DOI
https://doi.org/10.2298/TAM231221002E

Viscous dissipation effects in a vertical annulus filled with fluid-saturated porous medium
Eduard Marušić-Paloka and Igor Pažanin
Available online 05 June 2025

Abstract
The investigation of heat transfer within porous medium has attracted considerable interest because of its growing practical importance. The present paper is devoted to the study of a steady-state non-isothermal fluid flow through a vertical cylindrical annulus filled with sparsely packed porous medium. The governing system is given by the Darcy-Brinkman-Boussinesq model where the heat equation includes the viscous dissipation term. The side walls are maintained at uniform temperatures, while the flow is driven by the axial pressure gradient. Introducing the thickness of the annular region as the small parameter of the problem, the goal is to derive the approximation of the flow via asymptotic analysis. Although the governing problem is coupled and nonlinear, the asymptotic solution is proposed in the explicit form and that represents our main contribution. As such, it clearly displays the effects of porous structure and viscous dissipation on the temperature and velocity distribution. Due to the viscous dissipation, we observe the increase in the heat generation leading to a raise in the temperature and velocity profile within the annulus. Moreover, it is deduced that reducing the thickness of the annular region may be employed to strengthen the seepage velocity of the working fluid.

Mathematics Subject Classification
35B40, 35Q35, 76S05

Keywords
cylindrical annulus, viscous dissipation, porous medium, asymptotic analysis

DOI
https://doi.org/10.2298/TAM250311009M

Experimental study of tensor invariants of Hamiltonian systems
A. V. Tsiganov
Available online 27 August 2025

Abstract
Typically, one considers the problem of finding the minimum number of invariants of a dynamical system sufficient for integrability. It can be also assumed that there are invariants not related to integrability that describe other properties of the dynamical system. We compute such tensor invariants for some integrable and non-integrable dynamical systems by using modern computer software and discuss their properties.

Mathematics Subject Classification
58J70; 34A34, 70H05

Keywords
Hamiltonian systems, tensor invariants, superintegrable Kepler problem, non-integrable Hénon-Heiles system

DOI
https://doi.org/10.2298/TAM241217012T

High temperature solid mechanics: Mesoscale computational formulation
Siniša Đ. Mesarović
Available online 16 September 2025

Abstract
A mesoscale phase field formulation for high temperature computational mechanics of polycrystalline solids with voids is developed. The mathematical description includes translation and rotation of crystalline grains, diffusion through the crystals and interfaces, lattice growth at the boundary and grain boundary sliding, elastic stresses and compositional eigenstrains. The formulation connects heterologous continua; solids are represented by the lattice continuum, while the voids/gas are the standard mass continuum viscous (and elastically compressible) fluid. The deformation gradient for solids is consequently a state variable with evolution defined in the Eulerian sense. We consider non-inertial, controlled-temperature processes with vacancy-atom exchange diffusion mechanism and isotropic interface energies. Nevertheless, as discussed in the concluding section, the formulation provides the basis for extensions to the processes with significant heat sources or sinks, diffusion of multiple species and anisotropic interface energies.

Mathematics Subject Classification
74-10, 74A05, 74N25; 74A60, 74C20, 74F05

Keywords
sintering under stress, creep, grain growth, phase field, lattice continuum

DOI
https://doi.org/10.2298/TAM250605013M

On the quasi-diagonalization and uncoupling of damped circulatory multi-degree-of-freedom systems
Ranislav M. Bulatović and Firdaus E. Udwadia
Available online 29 September 2025

Abstract
The decomposition of linear multi-degree-of-freedom systems with damping, circulatory, and potential forces is considered through a real linear coordinate transformation generated by an orthogonal matrix. Criteria are derived that establish the conditions under which such a transformation exists, allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum dimension of two. These criteria are expressed in terms of the properties of systems' coefficient matrices. Several numerical examples are provided to demonstrate the analytical results.

Mathematics Subject Classification
70J10, 34A30

Keywords
linear multi-degree-of-freedom dynamical system, potential force, damping force, circulatory force, diagonalization and quasi-diagonalization, real change of coordinates, orthogonal transformation, dynamics, vibrations

DOI
https://doi.org/10.2298/TAM250108014B

Rolling geodesics on symmetric semi-Riemannian spaces
Velimir Jurdjevic
Available online 30 September 2025

Abstract
This paper is an outgrowth of the results in the domain of rolling obtained in our recent paper written with F.Silva Leite and I. Markina, and the earlier papers on the rollings of spheres produced with J. Zimmerman. We show that the rolling equations associated with a symmetric semi-Riemannian manifold rolling on its tangent space at a fixed point on the manifold essentially have the same structure as the rolling equations for the n-dimensional sphere rolling on the horizontal hyperplane; that is, we show that the rolling equations are described by a left-invariant distribution 𝒟 on a Lie group 𝐆 with the Lie bracket growth

𝒟+[𝒟,𝒟]+[𝒟,[𝒟,𝒟]]=T 𝐆,

Mathematics Subject Classification
53C17, 53C22, 53B21, 53C25, 30C80, 26D05; 49J15, 58E40

Keywords
Riemannian and semi-Riemannian manifolds, connections, parallel transport, isometries, Lie groups actions, Pontryagin maximum principle, extremal curves, integrable systems

DOI
https://doi.org/10.2298/TAM250408015J