551d76c7-6d0e-47eb-86dc-a2bb6796a36f 5 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Thiele . . . recapitulate stand alone section

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Trpo/Mesosphere
km[alt]/hPa[P] XY 1122713165151212055301140350 0.9 60 0.25 82 mat :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

X XY 1 col : Y XY 2 col : 12 mat support XY + 15 black plot : 21 sys

Clear K 0 : Table 0 : 12 mat

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 6 round vectorize :

... NUMERIC ...

K 227 0.032258 - 365.111111 - 0.306962 176.44208 - 0.012708 - 296.624465 1.883647 81 mat

round(K,6), is user from best fit. Most important, otherwise will create very large maple coeff's that ccan't be evaluated. round(K,6) typical for this Thiele.

CWD C:\SmathFile CurrentDirectory :

K CWD ThieleTreasury wfile 1

K CWD ThieleTreasury rfile :

Thiele on length of support points 'j' K X x Cfr j K rows 1 - : N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (1 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 61 line :

isolated 'K'

Recast inclusive of
parameters K's , X's x Cf K X x Cfr :

NUMERIC

SYMBOLIC

x f K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el / + / + / + / + / + / + / + :

J_Frac expansion demo

x last K 7 el x X 7 el - K 8 el / + confrac x convert evalf maple :

x last 5308850331 x * 10000000000 / 270080213310000000 / +

x last 270.080 0.530885 x * + ≡

Step: 1  ... Assign Symbolic ... Optimiz = NONE x collect x f confrac x convert evalf maple :

Step: 2 ... Expand Symbolic ... Optimiz = NONE x collect 2330303783 x * 5000000000 / 68947242310000000 / - 1518420663500000 x 3354266627500000000 / + 292922674310000000 x 48159403920000000 / - 6252855012500000 x 100920706750000000 / - (* / + (* / + (* / +

Step: 3 ...  eval the floating coefficients ... collect β 23303037835000000000 / 68947242310000000 / 3354266627500000000 / 48159403920000000 / 100920706750000000 / 1518420663500000 / 292922674310000000 / 6252855012500000 / 18 mat :

β transpose 0.466061 68.947242 6.708533 24.079702 20.184141 3036.841326 292.922674 250.1142 81 mat

Troposphere/Mesosphere J(β,"km")≡ "hPa" x J β 1 el x * β 2 el - β 6 el x β 3 el + β 7 el x β 4 el - β 8 el x β 5 el - / + / + / + :

altitude km 24 :

pressure hPa km J : 28.55

x λ 111 x ≤ (x 60 ≤ (& cases :

plot 16 - 1924019240192 km hPa 42 mat x J x λ * support 31 sys :

Trposphere/Mesosphere ... hPa vs km altitude

plot

km hPa 12 mat 24 28.55 12 mat