Determination of the Rotation Tensor in the Polar Decomposition

Keywords

Rotation (mathematics), Tensor (intrinsic definition), Mathematics, Mathematical analysis, Geometry

References

• Determination of C1/2, C-1/2 and more general isotropic tensor functions of CT. C. T. Ting — 1985
• Small strain and moderate rotationDomenico De Tommasi, Salvatore Marzano — 1993
• Small strain accompanied by moderate rotationP. M. Naghdi, L. Vongsarnpigoon — 1982
• Mechanics of Incremental DeformationM. A. Biot, D. C. Drucker — 1965
• On the vanishing of the additive measures of strain and rotation for finite deformationsLuiz Carlos Martins, R. F. de Oliveira, Paolo Podio–Guidugli — 1987
• Determination of the stretch and rotation in the polar decomposition of the deformation gradientAnne Hoger, Donald E. Carlson — 1984
• Comments on the paper: “Determination of the stretch and rotation in the polar decomposition of the deformation gradient” [Quart. Appl. Math. 42 (1984), no. 1, 113–117; MR0736511 (86a:73004)] by A. Hoger and D. E. CarlsonK. N. Sawyers — 1986

Cited by

• On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector SpacesC. S. Jog — 2002
• Derivatives and Rates of the Stretch and Rotation TensorsLuciano Rosati — 1999
• Polar rotation angle identifies elliptic islands in unsteady dynamical systemsMohammad Farazmand, George Haller — 2015
• On the use of homogeneous transformations to map human hand movements onto robotic handsGionata Salvietti, Monica Malvezzi, Guido Gioioso — 2014
• A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green∗Dongyan Tian, Jin Ming, Dui Guansuo — 2006
• Rigidity Constraints for Large Mesh DeformationYong Zhao, Xinguo Liu, Qunsheng Peng — 2009
• Derivatives of the Rotation and Stretch TensorsM. M. Carroll — 2004
• Invariants of C1∕2 in terms of the invariants of CAndrew N. Norris — 2007
• Direct determination of the rotation in the polar decomposition of the deformation gradient by maximizing a Rayleigh quotientCéline Bouby, Danielle Fortuné, Wojciech Pietraszkiewicz — 2005
• Explicit Representation of SO(3) Rotation Tensor for Deformable BodiesBohua Sun — 2020
• Explicit representation for the SO(3) rotation tensor of deformable bodiesBohua Sun — 2021
• Quadratic-stretch elasticityEduardo Vitral, James Hanna — 2021
• A reduced-order, rotation-based model for thin hard-magnetic platesYan Dong, Bastien F.G. Aymon, Pedro M. Reis — 2022
• Magneto-viscoelasticity of hard-magnetic soft-elastomers: Application to modeling the dynamic snap-through behavior of a bistable archEric M. Stewart, Lallit Anand — 2023
• Lagrangian gradient regression for the detection of coherent structures from sparse trajectory dataTanner D. Harms, Steven L. Brunton, Beverley McKeon — 2023
• On the direct determination of the right stretch tensor and the admissible region of its principal invariantsLászló Szabó — 2026
• On the direct determination of the right stretch tensor and the admissible region of its principal invariantsLászló Szabó — 2026
• J ul 2 02 1 Quadratic-stretch elasticityEduardo Vitral, J. Hanna — 2021
• Journal of the Mechanics and Physics of Solidsong Yan, Bastien F. G. Aymon, P. Reis — 2022

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