MATLAB: Finding unknown coefficients of a polynomial

polynomialsyms

Hi,
Matlab Version 2010b
I have a 7 degree polynomial function with unknown coefficients x=a0+a1*y+a2*y^2+a3*y^3+a4*y^4+a5*y^5+a6*y^6+a7*y^7
further y is a function of t : y=t^3
D_x means first derivative of x with respect to time (t)
DD_x means second derivative of x with respect to time (t)
I have the following values:
at t=t1
D_x=0 …. (1) DD_x=0 …. (2)
at t=t2
DD_x=0 ….(3)
at t=t3
DD_x=0 …..(4)
at t=t4
D_x+54*DD_x=0 …(5)
at t=t5
x+D_x*10+DD_x*54=12 …(6)
at t=t6
x + 87*DD_x=21 ….(7) D_x +89*DD_x=0 …(8)
so we have 8 equations and 8 unknowns (the unknown coefficients)
How do i find the values of a0 a1 a2 a3 a4 a5 a6 a7 in terms of t1 t2 t3 t4 t5 t6?
Please help me out. I hope I am clear

Best Answer

Pointing you in a reasonable direction...
syms t y a0 a1 a2 a3 a4 a5 a6 a7
syms t1 t2 t3 t4 t5 t6
x=a0+a1*y+a2*y^2+a3*y^3+a4*y^4+a5*y^5+a6*y^6+a7*y^7;
x = subs(x,y,t^3)
x =
a7*t^21 + a6*t^18 + a5*t^15 + a4*t^12 + a3*t^9 + a2*t^6 + a1*t^3 + a0
>> x1 = subs(diff(x,t),t,t1)
x1 =
21*a7*t1^20 + 18*a6*t1^17 + 15*a5*t1^14 + 12*a4*t1^11 + 9*a3*t1^8 + 6*a2*t1^5 + 3*a1*t1^2
See that x1 is simply a linear function of the a coefficients.
You can write each of your other equations as simple variations of the above. Then use solve.
John
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