1) Having the relation: r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t) where: a, b, c, d, h, k, m are real m > 0 t > 0 r > 0 "." represents multiplication sign
2) Is there a practical way (even with the help of a system Algebraic package) to derive the parametric relation between "m" on one side and the rest of parameters on the other side from the condition: r(t + 2pi.n) > r(t) where "n" is an integer > 0
> 1) Having the relation: > r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t) > where: > a, b, c, d, h, k, m are real > m > 0 > t > 0 > r > 0 > "." represents multiplication sign
> 2) Is there a practical way (even with the help of a system Algebraic > package) to derive the parametric relation between "m" on one side and > the rest of parameters on the other side from the condition: > r(t + 2pi.n) > r(t) > where "n" is an integer > 0
> Your expert help would be greatly appreciated.
> Regards. > Monir
Correction: =========== Independant variable "t" in item 1) of my OP should read: t >= 0
> On May 16, 4:27 pm, monir <mon...@mondenet.com> wrote:
> > Hello;
> > 1) Having the relation: > > r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t) > > where: > > a, b, c, d, h, k, m are real > > m > 0 > > t > 0 > > r > 0 > > "." represents multiplication sign
> > 2) Is there a practical way (even with the help of a system Algebraic > > package) to derive the parametric relation between "m" on one side and > > the rest of parameters on the other side from the condition: > > r(t + 2pi.n) > r(t) > > where "n" is an integer > 0
> > Your expert help would be greatly appreciated.
> > Regards. > > Monir
> Correction: > =========== > Independant variable "t" in item 1) of my OP should read: > t >= 0
> Regards. > Monir- Hide quoted text -
> - Show quoted text -
Hello; Here are some limited trial and error numerical results that satisfy the condition r(t+2pi.n) > r(t) where: r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t) The results do not cover all cases with all parameters since couldn't do such cases manually!
CASE 1: t-range 0 to 6.407576: a = 0.00101695 b = - 0.0004745 c = 0.00012327 d = 0 h = 0 k = 0 m = 0.10
CASE 2: t-range 0 to 10.2939339: a = 0.00146937 b = - 0.0002298 c = 3.3017E-05 d = 0 h = 0 k = 0 m = 0.10
CASE 3: t-range 0 to 16.8304665: a = 0.00232341 b = - 0.0003554 c = 5.6636E-05 d = -2.215E-06 h = 0 k = 0 m = 0.10
CASE 4: t-range 0 to 19.5654517: a = 0.00233668 b = - 0.0004121 c = 3.133E-05 d = -8.068E-07 h = 0 k = 0 m = 0.18
Your help in deriving the parametric relation(s) would be greatly appreciated.
