BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
buletinul institutului politehnic din iaşi - Universitatea Tehnică ...
buletinul institutului politehnic din iaşi - Universitatea Tehnică ...
- No tags were found...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 97<br />
that in the network nodes would be fulfilled the relation: f(l i ) = ξ i+1 = ξ i+1 (l i );<br />
L<br />
i= 0, n. It must be mentioned that l i<br />
= i ; i= 0, nand l 0 = 0; l n = L.<br />
n<br />
The classic algorithms for function interpolation upon exact data defined<br />
on a discreet lot of points are based on interpolative polynoms (for example,<br />
Lagrange, Newton, Stirling, Bessel polynoms).<br />
The use of these methods is difficult, due to some particularities in the<br />
field of application, and also due to the interpolation polynoms grade, equal to<br />
the n number of intervals. In such situation, the procedure increase in accuracy<br />
would be with a very complex mathematical device. For the simplicity was<br />
preferred an interpolation method with spline – function, which are – usually –<br />
polynomial function on portions. Most used spline functions are III-rd grade<br />
polynomial.<br />
On the [0, L] segment of the real axis attached to vehicle, a network of n<br />
equal intervals was build, separated by (n+1) equidistant points, in which nodes<br />
are specified the values of the function ξ i (l i ), i= 0, n. In the network nodes the<br />
L<br />
“length” variable takes the values l i<br />
= i , i= 0, n, with l 0 = 0; l n = L.<br />
n<br />
Cubic interpolation problem on portions requires the determination of a<br />
function f:[0, L]→ϒ; f = f(l) which satisfies the conditions:<br />
1) f(l) ∈ C 2 (0, L) that means that it is continuous along with it is II -nd<br />
grade derivatives including, on the definition interval. This condition suits the<br />
explicit interpretation of vehicles deformation.<br />
2) on each of the equal segments of the definition interval, [l i-1 , l i ] ,<br />
i= 1, n, the f(l) function is grade III polynom, with the form<br />
3<br />
i k<br />
f () 1 = fi() 1 = ∑ ak ( li<br />
−l)<br />
, i = 1 , n ; (1)<br />
k = 0<br />
3) in the network nodes the equalities are fulfilled<br />
( ) 1 ,<br />
f li<br />
ξ<br />
i +<br />
4) f // (l) satisfies the limit condition<br />
= i = 1,<br />
n ; (2)<br />
( 0) ( )<br />
= =0, i = 1,<br />
n . (3)<br />
// //<br />
f f L<br />
As the function f(l) second derivative is continuous and linear on each [l i--1 ,<br />
l i ] , i= 1, n interval of the network, it can be written that, for l i-1 ≤ l ≤ l i ( i= 1, n)