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As stated in the previously, one of the features that sets OOPSE apart |
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from most of the current molecular simulation packages is the ability |
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to handle rigid body dynamics. Rigid bodies are non-spherical |
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particles or collections of particles that have a constant internal |
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potential and move collectively.\cite{Goldstein01} They are not |
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included in many standard simulation packages because of the need to |
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consider orientational degrees of freedom and include an integrator |
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that accurately propagates these motions in time. |
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|
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Moving a rigid body involves determination of both the force and |
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torque applied by the surroundings, which directly affect the |
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translation and rotation in turn. In order to accumulate the total |
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force on a rigid body, the external forces must first be calculated |
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for all the interal particles. The total force on the rigid body is |
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simply the sum of these external forces. Accumulation of the total |
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torque on the rigid body is similar to the force in that it is a sum |
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of the torque applied on each internal particle, mapped onto the |
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center of mass of the rigid body. |
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|
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The application of the total torque is done in the body fixed axis of |
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the rigid body. In order to move between the space fixed and body |
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fixed coordinate axes, parameters describing the orientation be |
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maintained for each rigid body. At a minimum, the rotation matrix can |
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be described and propagated by the three Euler |
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angles.\cite{Goldstein01} In order to avoid rotational limitations |
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when using Euler angles, the four parameter ``quaternion'' scheme can |
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be used instead.\cite{allen87:csl} Use of quaternions also leads to |
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performance enhancements, particularly for very small |
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systems.\cite{Evans77} OOPSE utilizes a relatively new scheme that |
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propagates the entire nine parameter rotation matrix. Further |
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discussion on this choice can be found in Sec.~\ref{sec:integrate} |
