g = 9.8 k = 0.01 r = 0.006 R = 0.002 W = 6*2*Pi a = 3    s = NDSolve[{v'[t] ==  r*g*k*Cos[   Arg[W*R - w[t]*r*Cos[x[t]] - I*(v[t] + w[t]*r*Sin[x[t]])]] (Tan[     Arg[W*R - w[t]*r*Cos[x[t]] - I*(v[t] + w[t]*r*Sin[x[t]])]] -     Tan[x[t]]),     w'[t] ==  g*k*Cos[Arg[      W*R - w[t]*r*Cos[x[t]] - I*(v[t] + w[t]*r*Sin[x[t]])] -      x[t]]/r,     x'[t] ==  g*k*Sin[Arg[      W*R - w[t]*r*Cos[x[t]] - I*(v[t] + w[t]*r*Sin[x[t]])] -      x[t]]/(r*w[t]), x[0] == Pi/4, w[0] == 10, v[0] == -0.01}, {x,     w, v}, {t, a}, Method -> Automatic] 

“I used arctan instead of Arg but it caused problem like 135= -45(degree). So I changed arctan to Arg but I got the error. Can someone help me?”

NDSolve::ndinid: Initial condition 0.712979 -0.701185 I is not in the range specified by the discrete variable NDSolve`s$  60824.  NDSolve::ndinid: Initial condition 0.712979 -0.701185 I is not in the range specified by the discrete variable NDSolve`s$  60837.