Seminar Mechanics of Machines and Mechanisms - Models and Mathematical Methods

PROGRAM

Predavanja možete pratiti i online putem MITEAM stranice Seminara Mehanika mašina i mehanizama - modeli i matematičke metode: https://miteam.mi.sanu.ac.rs/asset/PgqjStRApvcGxwtBx

Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za MART 2026.

Sreda, 04.03.2026. u 12:00, sala 301f, Kneza Mihaila 36 i Live stream
Nenad Vesić, Mathematical Institute of the Serbian Academy of Sciences and Arts
GEOMETRY AND MECHANICS OF BIOLOGICAL GROWTH
Project presentation
The mechanics of growth is a field of study that continues to garner significant attention within the scientific community. This project aims to extend the conceptual framework of classical mechanics by integrating recent advancements in differential geometry, while maintaining a rigorous connection to established knowledge in the field.
The research is structured along two primary trajectories: 1) theoretical investigations and 2) the comparative analysis of derived results with experimental data through the methods of classical mechanics.
Drawing motivation from the monograph by Marsden (1983) and the seminal work of Yavari (2010), this study employs Riemannian spaces—where the affine connection coefficients are defined by Christoffel symbols—to represent the state of surfaces and bodies in the absence of external influences. Furthermore, we consider spaces of symmetric affine connection, characterized by coefficients equal to Christoffel symbols augmented by a prescribed symmetric tensor. By factorizing the difference between the affine connection coefficients in the initial and current states, the invariant geometric objects will be identified, providing a basis for a generalized action functional. Through the variation of the action with respect to the contravariant metric tensor, we establish the laws governing the curvature of the observed geometric objects as a result of intrinsic geometric shifts and environmental effects over time.
As a result of these considerations, the study elucidates the limitations of the linear model presented by Erlich and Zurlo (2025) in examining growth mechanics, thereby justifying the necessity of a quadratic model. The analysis of conformal deformations conducted by Yavari (2010) is further expanded by determining the corresponding invariants under the transformation of affine connections in two-dimensional and three-dimensional spaces. Additionally, analogous results are derived concerning F-planar, geodesic, and almost-geodesic mappings of the second and third type within these spaces.
Each theoretical result is complemented by computations supported by the principles of classical mechanics. This approach clearly demonstrates how differential geometry contributes to a more profound analysis of deformation mechanics, with particular emphasis on the mechanics of growth.
This research was supported by project O-40-26 of the Serbian Academy of Sciences and Arts, Branch in Niš.

Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.