ZigangPan/NonlinearSystems | Paclet Repository

ZigangPan`NonlinearSystems`

frobenius

sol=frobenius[ua,xc,x0] applies the Frobenius Theorem to a collection of vector fields stored in the matrix

ua

(every row is a vector field),

ua

is assumed to be involutive and nonsingular (at least locally around

x0

),

xc

is the state vector. It returns sol, which is a vector of functions of

xc

(formulas) of length Length[xc]-Length[ua], whose differentials are linearly independent and annihilates vector fields in

ua

.

Examples

(1)

Basic Examples

(1)

In[1]:=

ua={{1,-1,0,1,0},{-1,0,0,0,0},{2,-1,0,-1,0}};xc={x1,x2,x3,x4,x5};x0={0,0,0,0,0}

Out[1]=

{0,0,0,0,0}

In[2]:=

localinvolutiveQ[ua,xc,x0]

Out[2]=

True

In[3]:=

Frobenius[ua,xc,x0]

Out[3]=

{x3,x5}

SeeAlso

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RelatedGuides

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