Commun. Comput. Phys., 2 (2007), pp. 530-544.

Modified RATTLE Method for Rigid Body Dynamics in Cartesian Coordinates

Minxin Chen 1*

1 Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China.

Received 27 March 2006; Accepted (in revised version) 17 September 2006
Available online 4 December 2006


In this paper, we describe a modified RATTLE (M-RATTLE) method for rigid body dynamics directly in Cartesian coordinates. The M-RATTLE method introduces a new way of resetting the coordinates to satisfy the constraints at each step, which is designed for the rigid body dynamics calculations in the Cartesian coordinates. M-RATTLE is algebraically equivalent to the RATTLE method and the cost of performing rigid body dynamics by M-RATTLE is independent of the number of constraints. The interaction forces between atoms belonging to the same rigid molecule do not need to be computed and explicit expressions of the constraints of internal degrees of freedom are unnecessary. The performance and sampling results of the proposed method are compared with those of the symplectic splitting method for an isolated rigid benz molecule and for a cluster of twenty-seven benz molecules.

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PACS: 47.10.Df, 47.11.+j, 02.70.-c
Key words: Rigid body dynamics, RATTLE method, symplectic splitting method, Cartesian formulation.

*Corresponding author.
Email: (M. Chen)

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