To implement, in order to achieve the target r and bits, and the parameter value f and tau (namely r and phi known, f and tau unknown), and this need to solve nonlinear equations, I came out from the original equation evolution equations containing four unknowns, original equation is: f=SQRT ((cos (t) - f * cos (t + tau) + lambda cos (2 * t)) ^ 2 + (f * sin (t + tau) ^ 2), it is a force f t do equation of periodic change over time,

Equations for:

Tan (r) * cos (t2) - f * tan (r) * cos + tau (t2) + lambda tan (r) * cos (2 * t2) - f * sin (t2 + tau)=0.

(bits - 1) * (cos (t1) - f * cos (t1 + tau) + lambda cos (2 * t1)) - bits of * (cos (t2) - f * cos + tau (t2) + lambda cos (2 * t2))=0.

- sin (2 * t1) + 2 * f * sin (2 t1 + tau) - lambda * sin (t1) * cos (2 * t1) - f * sin (2 * t1 + 2 * tau)=0.

- sin (2 * t2) + 2 * f * sin (2 * t2 + tau) - lambda * sin (t2) * cos (2 * t2) - f * sin (2 * t2 + 2 * tau)=0,

F, tau, t1, t2 as unknowns, r, bits as known number, f, tau says six parameters, the t1 and t2 respectively f minimum, maximum when the corresponding time, equation is according to its location, f maximum equation 2 is the relation between the maximum and minimum value f, equations of three and four equations are original equation in t1 and t2 derivative is zero, just four equations of four unknowns,

But the problem is that the original equation of maximum minimum point is not the only, three and four equations cannot guarantee t1, t2 was respectively corresponding to the minimum and maximum time, so the system of equations is uncertain, hope people, give detailed programming steps, not on the basis of the nonlinear equations are given programming ideas, be obliged,

CodePudding user response:

Go to the algorithm version of q,,

CodePudding user response:

1) try to find out first , including boundary conditions, analysis (thinking),
2) to find the monotone interval, the mathematical problem is
3) in monotone interval , this programming solution,