The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...

One significant advantage Mathematica provides is that it can symbolically compute derivatives. This means that when you specify Method->"Newton" and the function is ...

Partition[list, n] partitions list into non-overlapping sublists of length n. Partition[list, n, d] generates sublists with offset d. Partition[list, {n_1, n_2, ...}] ...

Consider the matrix differential equation where the initial value y_0 y(0)∈^m×p is given. Assume that y_0^Ty_0I, that the solution has the property of preserving ...

The ability to generate pseudorandom numbers is important for simulating events, estimating probabilities and other quantities, making randomized assignments or selections, ...

DiscretePlot3D[expr, {i, i_min, i_max}, {j, j_min, j_max}] generates a plot of the values of expr when i runs from i_min to i_max and j runs from j_min to ...

It is often useful to be able to detect and precisely locate a change in a differential system. For example, with the detection of a singularity or state change, the ...

GraphCoordinates3D[g, options] calculates a visually appealing 3D layout of the vertices of a graph g and returns the coordinates of the vertices.

GraphCoordinates[g, options] calculates a visually appealing 2D layout of the vertices of the graph g and returns the coordinates of the vertices.