DIFFERENTIAL GEOMETRY, CONTINUUM MECHANICS AND MATHEMATICAL PHYSICS Seminar

 

PROGRAM

---

Predavanja možete pratiti i online putem MITEAM stranice seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika: https://miteam.mi.sanu.ac.rs/asset/YNvstaSeP9v2tgqTP

---

Plan rada seminara Diferencijalna geometrija, mehanika kontinuuma i matematička fizika za NOVEMBAR 2025.

---

Petak, 07.11.2025. u 12:15, Pariske Komune bb, Niš i Live stream
Aleksandar Obradović, Mašinski fakultet, Univerzitet u Beogradu
TIME MINIMIZATION DURING SIMULTANEOUS LONGITUDINAL AND ROTATIONAL MOTION OF A CHAPLYGIN SLEIGH
The problem of minization of the time of motion of a Chaplygin sleigh in the horizontal plane is analyzed. The force directed along the linear velocity vector and the torque are considered as control inputs. The use of the Pontryagin maximum principle allows for establishing that three types of control are possible: regular control, taking the boundary values (bang-bang) for the force and the torque, first-order singular control for the force, and second-order singular control for the torque. If the control is singular for the force on the entire interval, the solution of the optimization problem is not unique. The second-order control segment can be connected with nonsingular control only by means of the “chattering” regime. A simpler suboptimal control is proposed that contains a finite number of switchings. Examples are considered for the specified end states and partially specified end states. Analysis of possible combinations of singular and regular arcs of the trajectory is performed.

---

Petak, 14.11.2025. u 11:00, Pariske Komune bb, Niš i Live stream
Borislav Gajić, Matematički institut SANU
INTEGRABILNI MAGNETNI TOKOVI NA n-DIMENZINOJ SFERI I NEHOLONOMNA MEHANIKA
Uvode se i proučavaju Čapliginovi sistemi sa giroskopskim silama, čiju važnu podklasu čine sistemi sa magnetnim silama. Daje se uopštenje Demčenkovog slučaja kotrljanja giroskopske lopte po sferi, i posle redukcije se dobijaju Hamiltonovi magnetni sistemi na sferi. Konstruisan je Laksov par uz pomoć kojeg se pokazuje integrabilnost u proizvoljnoj dimenziji. Dobijeni integrali su prvog i drugog stepena po generalisanim impulsima.
Predavanje je zasnovano na zajedničkim radovima sa Vladimirom Dragovićem i Božidarom Jovanovićem.

---

Petak, 14.11.2025. u 13:00, Pariske Komune bb, Niš i Live stream
Božidar Jovanović, Matematički institut SANU
KONTAKTNI MAGNETNI GEODEZIJSKI I SUBRIMANOVI TOKOVI NA ${V_{\mathrm{n,2}}}^{}$ I INTEGRABILNI SLUČAJEVI TEŠKOG KRUTOG TELA SA GIROSKOPOM
Dokazujemo integrabilnost magnetnih geodezijskih tokova $\mathrm{SO}\left(n\right)$-invarijantnih Rimanovih metrika na Štifelovoj mnogostrukosti ranga dva ${V_{\mathrm{n,2}}}^{}$ u odnosu na magnetno polje dato standardnanom kontaktnom formom na ${V_{\mathrm{n,2}}}^{}$. Takođe, dokazujemo integrabilnost magnetnih sub-Rimanovih geodezijskih tokova za $\mathrm{SO}\left(n\right)$-invarijantne sub-Rimanove strukture na ${V_{\mathrm{n,2}}}^{}$. Svi rezultati se mogu posmatrati i bez uticaja magnetnog polja. Takođe razmatramo integrabilne prirodne mehaničke sisteme tipa matematičkog klatna sa kinetičkom energijom definisanom sa $\mathrm{SO}\left(n\right)\times \mathrm{SO}\left(2\right)$-invarijantnim Rimanovim metrikama. Za $n=3$, koristeći izomorfizam $V_{\mathrm{3,2}}\cong \mathrm{SO}\left(3\right)$, dobijeni integrabilni magnetni modeli svode se na integrabilne slučajeve kretanja teškog krutog tela sa giroskopom oko nepokretne tačke: giroskop Žukovskog-Voltere, Lagranžova čigra sa giroskopom i čigra Kovaljevske sa giroskopom. Kao nusproizvod dobijamo Laksove prezentacije za Lagranžovu čigru i čigru Kovaljevske u nepokretnom referentnom sistemu (dualne Laksove reprezentacije).
Zajednički sastanak sa Odeljenjem za mehaniku i Odeljenjem za matematiku. Petak, 28.11.2025. u 12:15, Pariske Komune bb, Niš i Live stream
Stepa Paunović, Matematički institut SANU
FRACTIONAL MAGNETO-VISCO-HYPERELASTICITY OF SOFT MREs – MODEL, RESULTS AND FUTURE OUTLOOKS
In this lecture we will discuss the motivation for research in the field of magneto-active soft (hyper)elastic materials and present the derived mechanical and mathematical model that can describe in much detail and precision the magneto-mechanical behaviour of this type of materials. We will also show how the non-integer order derivatives (commonly referred to as the fractional derivatives) can be included during the modelling process in order to obtain a more efficient and mathematically concise model. After presenting the mathematical model, we will briefly show how it was numerically implemented in the software FeniCSx, after which we will direct our attention to validation of the model by the experimental as well as numerical results from the literature, and show our results obtained by the numerical analysis done so far. We will conclude the lecture by summarizing the key points of the model and of the results, while emphasizing the drawbacks, limitations and introduced simplifications of the presented model. This would effectively pave the way for future research in this direction, leading to improvement of the model and the possibility to include several other physical fields and phenomena, thus enabling its wider practical application, especially in the field of soft robotics.
Zajednički sastanak sa seminarom Mehanika mašina i mehanizama - modeli i matematičke metode

---