I am associate professor at the Department of Mechanics Materials and Structures, Budapest University of Technology and Economics.
email: vpeter at mit.bme.hu

My research areass include structural mechanics, dynamics, nonlinear phenomena, as well as various biological, and geological applications of mechanics




Gömböc homepage




Force and form

Elective course

Contact dynamics: reality, models, paradoxes

Elective course




Ongoing research projects I am involved in:



Structural form finding


We examine the connection between structural geometry and behavior, with focus on moment-free structures


Collaborators: Mehmet Köhserli

Roof of the Great Court of British Museum
(Photo by DAVID ILIFF. License: CC BY-SA 3.0)


Nonlinear mechanics of soft strurctures
(NKFIH 124002)


We investigate the behavior of soft fibers subject to large deformations with focus on instability and applications in biology (root growth).


Collaborators: András A. Sipos

Experimental investigation of the instability of a slipping fiber

Rigid body dynamics in the presence of contacts.

(OTKA 104501, NKFIH 124002)

In this project, we focus on rigid bodies subject to friction and impacts. We seek to understand dynamical phenomena, singularities, inconsistency of rigid models (pl. Painlevé paradox), and stability properties of equilibria.


Collaborators: Alan R. Champneys, Arne Nordmark, Yizhar Or, Tamás Baranyai, Tamás Ther



What is Painlevé’s paradox? (in Hungarian)


A journal publication on Painlevé’s paradox and its full text.


Photo of experimental setup demonstrating that seemingly stable frictional equilibria may lack Lyapunov stability.

Internal dynamics of a slipping point contact in the presence of Painlevé’s paradox

Ulam’s floating body problem


Are there solids of density r other than the sphere that can float in any orientation (without turning)?’ – this problem was coined by Stanislav Ulam in the 1930s and recorded as problem 19 in the Scottish Book. Despite recent results pointing towards an affirmative answer, a full proof of their existence has not been given. I gave a constructive proof of their existence for density ˝ (PL Varkonyi, Stud. Appl. Math, to appear in 2013). Related questions about planar bodies (i.e. long logs with uniform cross-section) are also being examined (PL Varkonyi, Stud. Appl. Math, 2008)

A nontrivial neutrally floating solid of density 1/2. All examples I have found have rotational symmetry

Geometry, shape dynamics, and classification of particles subject to abrasive processes  (OTKA Grants 72146, 104601)


We analyze the geometrical properties of particles  (pebbles, sand, asteroids) in abrasive processes. Our goal is to understand their shape evolution as well as to work out statistical methods that provide information on the geological history of a particle set based on its geometrical properties


Collaborators: MTA-BME Morphodynamics Research Group, Julie E. Laity

Wind-worn rock (ventifact) with sharp edges, and flat faces. Photo: Matthias Bräunlich, Hamburg (www.kristallin.de)

The role of mechanical interactions in generating collective motion

(part of OTKA 72368 )


Groups of fish, birds, bacteria, and other moving creatures often show organized patterns, which are generated by simple interactions of individuals. The design of similar artificial systems is also a fast developing area of robotics. My goal is to understand, how collisions, contact, and collision avoidance strategies contribute to collective motion, and to learn about the propagation of information about motion preferences via mechanical interactions.


Collaborators: Research group of Tamás Vicsek



Simulation of self-propelled rigid objects subject

to attraction, and hard, inelastic collisions.

Click to plot to view video (9 MB, H.264 compression)


Objects that never capsize: mechanical and geometrical aspects of spontaneous self-righting


If dropped onto a plane, most objects stop in one of several stable equilibrium positions. Alternatively they may not stop at all, if the plane is not horizontal. Our goal is to design, and analyze self-righting objects that do stabilize in a unique position regardless of the initial conditions. The existence of such shapes not only represents intriguing mathematical questions, but it has a wide field of application from biomorphology to robotics.


Collaborators: Gábor Domokos, Roger W. Benson 



An object that does capsize: Benő the turtle