0ffa1d7b-da0a-4715-af8f-c97454bcfe30 39 4 5 decimal

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

Martin conclusive solve block 4.99100867349489 1017^* 202339247180557 / kg m 2^* s 2^/ * 595000003 / kg m s 2^* / * 11 ε 2 / - (2^- (* 0 ε < (ε 2 < (& 595000003 / kg m s 2^* / * ε 0 ≥ 0 cases ε 0 x int 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases 69500 / * / 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases * 1 * m 20 / * 3 m * 10 / * 7.19445827947879 1015^* 1.10911303855442 1016^* / * m 20 / * + 3000 kg * m 2^* s 2^/ ≡ x Solve

4.99100867349489 1017^* 202339247180557 / kg m 2^* s 2^/ * 3000 kg * m 2^* s 2^/ - 533.3462 J * -

kg 1 m * s 2^* / Pa

kg m 2^* s 2^/ J

1 m 20 / * 3 m * 10 / * 7.19445827947879 1015^* 1.10911303855442 1016^* / * m 20 / *

Recast the solve block wrt 'x' 533.3462 J * - ε Integrand ε 0 x int x D / x f * + 0 ≡ x solve

u F 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases :

0.0035 m 3^* explained below ≡

z ∫ u F u 0 x int :

x ∫ z ∫ :

conclusive solve block ∫(x)=> type conversion error 2466.6538 J * 0.0035 m 3^* x ∫ * + 3000 J * ≡ x Solve

0.0035 x ∫ *

1 ∫ 1.4875 107^* Pa *

============ Re-process the solve block as discrete ===========

ε Integrand 14875000 kg * 42 ε - (2^- (* 3 m * s 2^* / 0 ε < (ε 2 < (& 59500000 kg * 3 m * s 2^* / ε 0 ≥ 0 cases :

x 1012 -^2 0.00625 range :

Discrete Integrand DI x x Integrand vectorize augment :

x Integrand DI

x Integrand vectorize kg m s 2^* / /

x f 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases 1 m 20 / * 3 m * 10 / * 7.19445827947879 1015^* 1.10911303855442 1016^* / * m 20 / * (* :

x D 595000003 / kg m s 2^* / * 11 x 2 / - (2^- (* 0 x < (x 2 < (& 595000003 / kg m s 2^* / * x 0 ≥ 0 cases 69500 / * :

x f x D / vectorize 0.0035 m 3^* ≡

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

DI Σ

Σ DI Σ 2 col :

Discrete system wrt 'x' System x 0.0035 m 3^* Σ * augment :

533.3462 J * -

Test 50000 :

System 533.3462 - Test 1.37 100000 1.37 0 2 2 mat 4 1 sys

Solving the original "Solve block" resumes to find the value of 'x' in the discrete system from the given -533.3462J. ANSWER: no solution The system is "ill posed" for a solution. The system is solvable in the positive quadrant

X System 1 col : Y System 2 col : 21 line

Locating the first occurrence of a specific element in a vector

v x search j 1 : v j el x ≤ j j 1 + : while j v j el 12 mat 31 line :

Sol Y 50000 J * search : 22050191 kg m 2^* s 2^/ * 12 mat

idx Sol 1 col :

x System idx 1 el : 1.3687 11 mat

1. The project solution is "ill posed" somewhere in the "Engineering procedure". 2. For a more refined solution 'x'=> discretise finer the integrand. 3. The "System" in this document results in an export data table. ----------------------------------------------------------------- Solving for 'x' given 'y' in the system is equivalent to inversing the system, similar to "InverseFunction" in continuous function(s)... example: Probit. If 'System' is a constant curve wrt the Engineering concerned, it seems feasible to find a good model function. On that last point, I'm willing to exercise this proposal.

vx vy chr sz clr plotG n vx length : plot vx 1 el vy 1 el chr sz clr augment : i 2 n range plot plot vx i el vy i el chr sz clr augment stack : for plot 41 line :

data 11012 -^* 0 0.025 22 0.05 86 0.075 193 0.1 341 0.125 531 0.15 761 0.175 1032 0.2 1342 0.225 1691 0.25 2078 0.275 2504 0.3 2967 0.325 3467 0.35 4003 0.375 4575 0.4 5182 0.425 5824 0.45 6500 0.475 7210 0.5 7953 0.525 8728 0.55 9536 0.575 10375 0.6 11244 0.625 12145 0.65 13074 0.675 14034 0.7 15022 0.725 16038 0.75 17082 0.775 18153 0.8 19250 0.825 20374 0.85 21523 0.875 22697 0.9 23895 0.925 25117 0.95 26363 0.975 27631128922 1.025 30234 1.05 31568 1.075 32922 1.1 34296 1.125 35689 1.15 37102 1.175 38533 1.2 39982 1.225 41448 1.25 42931 1.275 44431 1.3 45946 1.325 47476 1.35 49021 1.375 50580 1.4 52153 1.425 53738 1.45 55336 1.475 56946 1.5 58568 1.525 60200 1.55 61842 1.575 63495 1.6 65156 1.625 66826 1.65 68505 1.675 70191 1.7 71884 1.725 73583 1.75 75289 1.775 76999 1.8 78715 1.825 80435 1.85 82159 1.875 83886 1.9 85616 1.925 87348 1.95 89082 1.975 90817292552812 mat :

Prepare the Poly model

data n Decimate collects every 'n' points range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

x φ x x 2^x 3^31 mat :

XY data 9 Decimate : X XY 1 col : Y XY 2 col : 31 line

j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 41 line

b 1.8076 - 34708.3332 5784.7222 - 31 mat

x f b x φ * :

<= recast the scalar model

data X Y . 11 black plotG :

x Y 50000 :

sol x f x Y - 0 ≡ x 15 solve : 1.3657

data x f x Y sol 100000 sol 0 2 2 mat 4 1 sys

f L H N Inverse dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range sol j el x f ω j el - 0 ≡ x 0 2.05 solve eval : for ω sol augment 41 line :

Inv f 09255250 Inverse :

Inv

Project reconciliation

0 ... 30000 α 3.438 105 -^* 0.534 21 mat :

0 ... 92552 β 3.453 105 -^* 0.595 21 mat :

'data' [above] is the solution to the "Solve" given block. It solves 'x' for user "steel J". The solution reads left <= right [x <= J]. It is in fact the final Engineering table for any one to carry in-situ. The table may be populated at will. By same token 'data' is the sole document that will pass the QA approval [Quality Assurance]. For sake of completing the project, 'sol(x)' gives the direct solution from the InverseFunction ... for convenience. -------------------- My understanding is : 'x'= m^3/ 'steel J' -------------------- Observe: 'data' can be tabulated J => x

Inv Inv 3 Decimate :

x sol α 1 el x * (α 2 el^0 x ≤ (x 30000 ≤ (& β 1 el x * (β 2 el^cases :

X Inv 1 col : Y Inv 2 col : 21 line

xy X Y . 10 red plotG :

x sol xy 2 1 sys