Re: Non linear system solving

*To*: mathgroup at smc.vnet.net*Subject*: [mg71432] Re: [mg71369] Non linear system solving*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Sat, 18 Nov 2006 04:41:03 -0500 (EST)*References*: <200611160552.AAA08230@smc.vnet.net>

er, one more thing: I am assuming your question was, "How do I make sure the answers for FindRoot won't jump to a different branch as I am iterating my solution?". On 11/15/06, Jean-Paul <Jean-Paul.VINCENT-3 at etudiants.ensam.fr> wrote: > Dear Group, > I'm a french student working on gears, particulary on gear engagement. > To summerize quickly: > The active surfaces of a gear teeth are made to ensure an homokynetic > (homokinetic) transmission. > We have, in theory, > a1/a2=constant, with ai, the rotation angle of the part i. > My work is to find this relation: > First the surfaces are represented by equations ( a 3D Vector, with two > parameters) in a local coordinate system. > These parameters are u1 and v1 for the gear 1, u2 and v2 for the gear > 2. > To simulate the transmission between these gears, we write these > equations in a common coordinate system, giving them another parameter, > for the position , the angle of rotation, a1 and a2. > So for the gear 1, we have: > s1(u1,v1,a1) > Active surface for the gear 2 is given by: > s2(u2,v2,a2) > > To simulate the engaging, we have to translate mathematically the > contact between the two surfaces: > > First condition: > > Surfaces are in contact, that leads to: > > > s1(u1,v1,a1)=s1(u2,v2,a2) -> 3 equations. > > Second condition: > > The normals at the contact point are parallel. > > n1(u1,v1,a1)=k.n2(u2,v2,a2) ->3 equations, one more unkown introduced: > k > > Finaly: we have 6 Equations, and 6 unknowns (u1,v1, u2, v2, a2, k) > Theses equations are too complicated, to obtain an explicit solution. > We have to divide the problem: > Solve the non linear system, for each value of a1. > Then we have several couple of (a1,a2). > > This is the context of my work. > I tried to write in Mathematica, using the famous function "Findroot". > > My question begin here: > > Findroot works well, but when the relative curvatures of the surfaces > near the contact point are close, the fonction shows its limit. > I began to write a program, calculating the Jacobian Matrix of the > system and by iteration i found a solution vector. > The solutions found are not in the interval. > Indeed parameter of the surface v1 varies between 50 and 100. > The solution given by Mathematica is 0. > The FindRoot function allows us to give interval for all unknowns (and > gives 83.3 for v1 (example) if we give the interval, 0 if not). > > Can someone, help me to make a program witch take into account > intervals for each unknown? > I am asking for a program, just the mathematical part. > Thank You very much. > > Best Regards > > PS: Please excuse my bad English. > > -- http://chris.chiasson.name/

**References**:**Non linear system solving***From:*"Jean-Paul" <Jean-Paul.VINCENT-3@etudiants.ensam.fr>