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Interaction between an edge dislocation and a rigid hypotrochoidal inhomogeneity

Wang X., Schiavone P.

Archives of Mechanics

2024

Vol. 76, nr 1-2

143--153

We study the plane elasticity problem associated with a rigid hypotrochoidal inhomogeneity embedded in an infinite isotropic elastic matrix subjected to an edge dislocation located at an arbitrary position. A closed-form solution to the problem is derived primarily with the aid of conformal mapping and analytic continuation. All of the unknown complex constants appearing in the pair of analytic functions characterizing the elastic field in the matrix are determined in an analytical manner. In addition, a simple method distinct from that by Santare and Keer (1986) is proposed to determine the rigid body rotation of the rigid inhomogeneity.

Relativistic rotation of the rigid body in the Rodrigues-Hamilton parameters: Lagrange function and equations of motion

Pashkevich V. V., Eroshkin G. I.

Artificial Satellites : Journal of Planetary Geodesy

2018

Vol. 53, No. 3

89--115

The main purposes of this research are to obtain Lagrange function for the relativistic rotation of the rigid body, which is generated by metric properties of Riemann space of general relativity and to derive the differential equations, determining the rigid body rotation in the terms of the Rodrigues-Hamilton parameters. The Lagrange function for the relativistic rotation of the rigid body is derived from the Lagrange function of the nonrotation point of masses system in the relativistic approximation.