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1 results about "Axis–angle representation" patented technology
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In mathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle θ describing the magnitude of the rotation about the axis. Only two numbers, not three, are needed to define the direction of a unit vector e rooted at the origin because the magnitude of e is constrained. For example, the elevation and azimuth angles of e suffice to locate it in any particular Cartesian coordinate frame.
A method for efficiently and stably simulating non-stretchable ropes in a crane or hoist
ActiveCN115818443BSustainable transportationLoad-engaging elementsAxis–angle representationQuaternion
The present invention discloses a high-efficiency and stable method for simulating inextensible ropes in crane and hoist. The piecewise linear inextensible rope is usually represented by the Cartesian coordinates of the vertices and the quaternions on the segments, which uses too many degrees of freedom and needs many constraints, bringing unnecessary numerical difficulties and computational burden to the simulation. The present invention proposes a compact representation which uses the minimum number of degrees of freedom and naturally satisfies all the additional constraints. Specifically, the rope is regarded as a chain of rigid segments, and its shape is encoded as the Cartesian coordinates of its root vertex and the axis-angle representation of the local coordinate system on each segment. Under the representation of the present invention, the implicit time-stepping matrix has a special non-zero pattern. Using the non-zero pattern, the present invention designs a preconditioner which can solve the related linear equations with approximate linear complexity, and its speed is improved by one to two orders of magnitude compared with the widely used block-diagonal linear PCG solver.
Owner:ZHEJIANG UNIV