how to get Parameters of nonlinear function by passing pairs of values to it

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Bass Tea 2021-7-9

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https://ww2.mathworks.cn/matlabcentral/answers/875633-how-to-get-parameters-of-nonlinear-function-by-passing-pairs-of-values-to-it

编辑： Bass Tea 2021-7-10

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hey there,

i have another stupido question =) :

imaging i've got a polynomial function like this

i can retrieve

by using 3 pairs of values got from auxilliary points like

with following equation system...

(edit 1):

and this is vectorial notation...

;

leads to

and so

% code to doing so:
syms C1 C2 C3; A=[0 0 1;4 2 1;16 4 1]; t=[C1;C2;C3]; b=[0;6;7]; t=A^(-1)*b

So far so good.

But now, i'm analysing a coast down experiment. My differential equation is like this

, where n is meant to be the rotational speed of driving wheels in

, t is time in

and

are coefficients, based on resitive torques from rolling resistance, acceleration resistance, air drag and so on. When i put it into MATLAB i got the solution

So far so good. Now, theoretically, when i drive a test run on the road and want to point out

, i'm logging speed over time. So i have tons of data pairs to determine

But how can i extract this from that differential equation solution?

% code to experiment
clear; close all; format shortG
syms n(t) A B C D;
eqn = diff(n,t,1) == -A/D*n^2 - B/D*n - C/D 
cond = n(0) == 950/60; % start speed 950 [rpm] into [rps]
...nSol(t) = dsolve(eqn,cond,'Implicit', true)
nSol(t) = dsolve(eqn,cond)
nSol = simplify(nSol)