# Question:Error, (in DEtools/convertsys) unable to convert to an explicit first-order system

## Question:Error, (in DEtools/convertsys) unable to convert to an explicit first-order system

Maple

I have a system of equations:

`> c := .67;print(`output redirected...`); # input placeholder                                    0.67> r := `<,>`(r1, r2, r3);print(`output redirected...`); # input placeholder                       Vector[column](%id = 190246956)> Y := `<,>`(gamma1(t), gamma2(t), gamma3(t));print(`output redirected...`); # input placeholder                       Vector[column](%id = 190247020)> r1 := piecewise(gamma3(t) > c, -gamma1(t), -.74*sin(`&varphi;`(t)));print(`output redirected...`); # input placeholder       piecewise(0.67 < gamma3(t), -gamma1(t), -0.74 sin(&varphi;(t)))> r2 := piecewise(gamma3(t) > c, -gamma2(t), gamma3(t) <= c, -.74*cos(`&varphi;`(t)));print(`output redirected...`); # input placeholder         piecewise(0.67 < gamma3(t), -gamma2(t), gamma3(t) <= 0.67,            -0.74 cos(&varphi;(t)))> r3 := piecewise(gamma3(t) > c, c-gamma3(t));print(`output redirected...`); # input placeholder                piecewise(0.67 < gamma3(t), 0.67 - gamma3(t))> dr1 := piecewise(gamma3(t) > c, -(diff(gamma1(t), t)), -.74*cos(`&varphi;`(t))*(diff(`&varphi;`(t), t)));print(`output redirected...`); # input placeholder                         /                    d                             piecewise|0.67 < gamma3(t), ---- gamma1(t),                          \                    dt                                                     / d             \\                  -0.74 cos(&varphi;(t)) |--- &varphi;(t)||                                         \ dt            //> dr2 := piecewise(gamma3(t) > c, -(diff(gamma2(t), t)), .74*sin(`&varphi;`(t))*(diff(`&varphi;`(t), t)));print(`output redirected...`); # input placeholder                         /                    d                             piecewise|0.67 < gamma3(t), ---- gamma2(t),                          \                    dt                                                    / d             \\                  0.74 sin(&varphi;(t)) |--- &varphi;(t)||                                        \ dt            //> dr3 := piecewise(gamma3(t) > c, -(diff(gamma3(t), t)));print(`output redirected...`); # input placeholder                          /                    d           \                 piecewise|0.67 < gamma3(t), ---- gamma3(t)|                          \                    dt          /> epsilon := zs(t)+evalm(`&*`(r, Y));print(`output redirected...`); # input placeholderzs(t)   + piecewise(0.67 < gamma3(t), -gamma1(t), -0.74 sin(&varphi;(t))) gamma1(t) +   piecewise(0.67 < gamma3(t), -gamma2(t), gamma3(t) <= 0.67,   -0.74 cos(&varphi;(t))) gamma2(t)   + piecewise(0.67 < gamma3(t), 0.67 - gamma3(t)) gamma3(t)> n := piecewise(epsilon > 0, 0, epsilon < 0, -100*epsilon, epsilon = 0, N);> print(??); # input placeholderprint(??); # input placeholder> N := (r2*(diff(omega3(t), t))-r3*(diff(omega2(t), t))+dr2*omega3(t)-dr3*omega2(t))*gamma1(t)+(r3*(diff(omega1(t), t))-r1*(diff(omega3(t), t))+dr3*omega1(t)-dr1*omega3(t))*gamma2(t)+(r1*(diff(omega2(t), t))-r2*(diff(omega1(t), t))+dr1*omega2(t)-dr2*omega1(t))*gamma3(t)+(omega2(t)*r3-omega3(t)*r2)*(omega2(t)*gamma3(t)-omega3(t)*gamma2(t))+(omega3(t)*r1-omega1(t)*r3)*(omega3(t)*gamma1(t)-omega1(t)*gamma3(t))+(omega1(t)*r2-omega2(t)*r1)*(omega1(t)*gamma2(t)-omega2(t)*gamma1(t)+1);> > > > > > print(??); # input placeholder> eq := {.19*(diff(omega3(t), t))+r1*u2(t)-r2*u1(t)-n*(r1*gamma2(t)-r2*gamma1(t)) = 0, .114*(diff(omega1(t), t))+0.76e-1*omega2(t)*omega3(t)+r2*u3(t)-r3*u2(t)-n*(r2*gamma3(t)-r3*gamma2(t)) = 0, .114*(diff(omega2(t), t))-0.76e-1*omega3(t)*omega1(t)+r3*u1(t)-r1*u3(t)-n*(r3*gamma1(t)-r1*gamma3(t)) = 0, diff(u1(t), t)+omega2(t)*u3(t)-omega3(t)*u2(t)+u1(t)+r2*(diff(omega3(t), t))-r3*(diff(omega2(t), t))+dr2*omega3(t)-dr3*omega2(t)+(omega3(t)*r1-omega1(t)*r3)*omega3(t)-(omega1(t)*r2-omega2(t)*r1)*omega2(t)-(n-1)*gamma1(t) = 0, diff(u2(t), t)+omega3(t)*u1(t)-omega1(t)*u3(t)+u2(t)+r3*(diff(omega1(t), t))-r1*(diff(omega3(t), t))+dr3*omega1(t)-dr1*omega3(t)+(omega1(t)*r2-omega2(t)*r1)*omega1(t)-(omega2(t)*r3-omega3(t)*r2)*omega3(t)-(n-1)*gamma2(t) = 0, diff(u3(t), t)+omega1(t)*u2(t)-omega2(t)*u1(t)+u3(t)+r1*(diff(omega2(t), t))-r2*(diff(omega1(t), t))+dr1*omega2(t)-dr2*omega1(t)+(omega2(t)*r3-omega3(t)*r2)*omega2(t)-(omega3(t)*r1-omega1(t)*r3)*omega1(t)-(n-1)*gamma3(t) = 0, u1(0) = 0, u2(0) = 0, u3(0) = 0, zs(0) = .3367, diff(zs(t), t) = -(omega2(t)*r3-omega3(t)*r2)*gamma1(t)-(omega3(t)*r1-omega1(t)*r3)*gamma2(t)-(omega1(t)*r2-omega2(t)*r1)*gamma3(t), diff(gamma1(t), t) = -omega2(t)*gamma3(t)+omega3(t)*gamma2(t), diff(gamma2(t), t) = -omega3(t)*gamma1(t)+omega1(t)*gamma3(t), diff(gamma3(t), t) = -omega1(t)*gamma2(t)+omega2(t)*gamma1(t), diff(`&varphi;`(t), t) = omega3(t)-(omega1(t)*gamma1(t)+omega2(t)*gamma2(t))*gamma3(t)/(1-gamma3(t)^2), gamma1(0) = 0, gamma2(0) = (1-.99^2)^(1/2), gamma3(0) = .99, omega1(0) = 0, omega2(0) = 0, omega3(0) = 1, `&varphi;`(0) = 0};print(??); # input placeholder> print(??); # input placeholder> syst := dsolve(eq, [gamma1(t), gamma2(t), gamma3(t), `&varphi;`(t), u1(t), u2(t), u3(t), omega1(t), omega2(t), omega3(t), zs(t)], numeric, maxfun = 500000);%;Error, (in DEtools/convertsys) unable to convert to an explicit first-order system> syst(55);`
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`so, the problem is in piecewise function n: when n:=N it works, but in this case i can't model a problem with losing touch`
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