Similarity, Symmetry and Group Theoretical Methods in Mechanics - CURRENTLY NOT SCHEDULED

Suggested readings

G. Bluman, A. Cheviakov, S. Anco. Applications of Symmetry Methods to Partial Differential Equations, Appl. Math. Sci. vol. 168, Springer, New York 2010, 417pp.

G. Bluman, A. Cheviakov, J.F. Ganghoffer. ‘Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics’. Int. J. Engng Math. 2008. DOI 10.1007/s10665–008-9221–7.

V. Magnenet, R. Rahouadj, J.F. Ganghoffer, C. Cunat. Continuous symmetries and constitutive laws of thermo-elasto(visco)plastic materials within a thermodynamical framework of relaxation. Part I: formal aspects. Int. J. Plasticity, 23, Issue 1, 2007, 87–113.

A. Cheviakov, J.F. Ganghoffer. Symmetry Properties of Two- Dimensional Ciarlet-Mooney-Rivlin Constitutive Models in Nonlinear Elastodynamics. Journal of Mathematical Analysis and Applications. 2012. 396, 625–639.

J.F. Ganghoffer, V. Magnenet, R. Rahouadj. Relevance of symmetry methods in mechanics of materials. Int. J. Engng Math., 66, 103–119, 2010.

I. Mladenov, New Solutions of the Shape Equation, Eur. Phys. J. B 29, 327–330, 2002.

A. Müller, J. Rico: Mobility and Higher Order Local Analysis of the Mechanisms, in: J. Lenarcic, P. Wenger (eds.), Advances in Robot Kinematics, 2008, Springer, pp. 215–224.

A. Müller: On the Manifold Property of the Set of Singularities of Kinematic Mappings: Modeling, Classification, and Genericity, ASME Trans., Journal of Mechanisms and Robotics, vol. 3, 2011.

J.J. Slawianowski. Geometry of Phase Spaces. Wiley & Sons, 1991.

J. J. Slawianowski. The Mechanics of the Homogeneously Deformable Body. Dynamical Models with High Symmetries. Zeitschrift für angewandte Mathematik und Mechanik 62: 229 – 240, 2006. doi:10.1002/ zamm.19820620604.

V. Vassilev, I.M. Mladenov, Geometric Symmetry Groups, Conservation Laws and Group-Invariant Solutions of the Willmore Equation, Geometry, Integrability and Quantization 5, 246–265, 2004.


See also