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Joint Chinese-Russian Mathematical Online Colloquium

Organizing Committee

  • Huijun Fan (SMS PKU)
    symplectic geometry and mathematical physics, geometric analysis
  • Sergey Gorchinskiy (MI RAS)
    algebra and geometry: algebraic geometry, K-theory
  • Hailiang Li (SMS CNU)
    fluid mechanics, partial differential equations, analysis
  • Jinsong Liu (AMSS)
    algebraic geometry: singularity theory
  • Yi Liu (BICMR)
    Topology of 3-manifolds, hyperbolic geometry
  • Denis Osipov (MI RAS)
    algebraic geometry, number theory, integrable system
  • Ye Tian (UCAS, AMSS)
    Number Theory, Arithmetic Geometry, Iwasawa Theory
  • Alexey Tuzhilin (MSU)
    geometry: Riemannian and metric geometry
  • Yue Yang (CE PKU)
    computation mathematics and mechanics
  • Ping Zhang (AMSS)
    P. D. E.: fluid equation and semi-classical analysis
  • Alexander Zheglov (MSU)
    geometry: algebraic geometry, integrable system


11:00 (GMT+3)
  Xuefeng Wang
Peking University

Bio: Xuefeng Wang is an Assistant Professor at College of Engineering, Peking University. He received the Ph.D. degree from University of Maryland, Baltimore County, USA, in 2017. He received the first prize of the paper competition in ASME and best paper award in IEEE conferences. His research interests are exoskeleton robots, surgical robots, unmanned vehicles, multibody dynamics and Control.

Self-Stabilization Mechanism Analysis of Bicycle Nonholonomic System.

A bicycle is a typical nonholonomic system, and the nonholonomic constraints attribute to different non-straightforward dynamic phenomena to the bicycle. Self-stabilization, i.e., the bicycle can move in balance without external assistance, is an interesting phenomenon, yet its mechanism is unclear due to complex interactions of the constrained bicycle multibody dynamics. We study the self-stabilization from two aspects: stability analysis and mechanism analysis. In the stability analysis, by the physical understanding of the bicycle system, we establish a dimension-reduction method to calculate the nontrivial equilibria of the highly nonlinear and high-dimensional differential algebraic equations (DAEs). Furthermore, we propose an implementable procedure to conduct stability analysis of the equilibria, where linearization of the DAEs is performed first and then the dimensionality reduction is followed. In the mechanism analysis, we obtain a reduced bicycle dynamic model based on the geometric symmetries and cyclic coordinates, which theoretically transforms the complex DAEs to a clear model structure without constraints. Based on the reduced model structure, we develop a bicycle surrogate model and establish comprehensive and quantitative understanding of the self-stabilization mechanism. The analysis shows that the nonholonomic constraints play important roles by providing anti-falling torques, equivalent stiffness and damping factors in the stabilization of the bicycle system.



12:00 (GMT+3)
  Sergey Bolotin

Bio: Sergey Bolotin is a specialist in Hamiltonian systems, variational methods and celestial mechanics. He is a corresponding member of the Russian Academy of Sciences. He was an invited speaker at ICM 1994 in Zürich at the section "Ordinary Differential Equations". He is a principal scientific researcher at the Steklov Mathematical Institute of RAS and also a head of the department of mechanics. He is a professor at Moscow State University. He was a professor at University of Wisconsin-Madison, USA, and is now professor emeritus there.

Dynamics of slow-fast Hamiltonian systems.

Slow-fast Hamiltonian systems appear in many applications, in particular in the problem of Arnold's diffusion. When the slow variables are fixed we obtain the frozen system. If the frozen system has one degree of freedom and the level curves of the frozen Hamiltonian are closed, there is an adiabatic invariant which governs evolution of the slow variables. Near a separatrix of the frozen system the adiabatic invariant is destroyed. A.Neishtadt proved that at a crossing of the separatrix the adiabatic invariant has "random" jumps and the slow variables evolve in a quasi-random way. In this talk we discuss partial extension of Neishtadt's results to multidimensional slow-fast systems. The slow variables shadow trajectories of an effective Hamiltonian system which depends on a "random" integer parameter.

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Meeting ID:638-406-013