<p> piecewise construct </p>

69fb2a9c-e78b-4937-803f-28f5c7c01acc 16 4 5 decimal

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

ρ.a 7850 : α.c 25 : σ 5.67 108^/ : 31 line

ratio.Am.b_V 70102^* : ratio.Am_V 107102^* : k.sh 0.9 ratio.Am.b_V ratio.Am_V / * : 31 line

Φ 1.0 : ε.m 0.7 : ε.f 1.0 : 31 line

ratio.Am.b_V ratio.Am_V k.sh 31 mat 700010700 0.5888 31 mat

θ.a c.a1 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + : θ.a c.a2 66613002738 θ.a - / + : θ.a c.a3 54517820 θ.a 731 - / + : θ.a c.a4 650 : 41 sys

t θ.g 203458 t * 1 + log10 * + :

t θ.a D.1 k.sh θ.a c.a1 ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* : t θ.a D.2 k.sh θ.a c.a2 ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* : t θ.a D.3 k.sh θ.a c.a3 ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* : t θ.a D.4 k.sh θ.a c.a4 ρ.a * / ratio.Am_V * α.c t θ.g θ.a - (* Φ ε.m * ε.f * σ * t θ.g (4^θ.a 4^- (* + (* : 41 sys

t.init 0 : t.12 24.4 : t.23 35.8 : t.34 54.7 : t.final 120 : steps t.final : 61 line

res.1 20 t.init t.12 steps t θ.a D.1 dn_GearsBDF : res.2 600 t.12 t.23 steps t θ.a D.2 dn_GearsBDF : res.3 735 t.23 t.34 steps t θ.a D.3 dn_GearsBDF : res.4 900 t.34 t.final steps t θ.a D.4 dn_GearsBDF : 41 sys

<p> piecewise construct </p>

time.1 res.1 1 col : temp.1 res.1 2 col : 12 mat θ.a.cr t.1 temp.1 time.1 θ.a.cr ainterp : 21 line time.2 res.2 1 col : temp.2 res.2 2 col : 12 mat θ.a.cr t.2 temp.2 time.2 θ.a.cr ainterp : 21 line time.3 res.3 1 col : temp.3 res.3 2 col : 12 mat θ.a.cr t.3 temp.3 time.3 θ.a.cr ainterp : 21 line time.4 res.4 1 col : temp.4 res.4 2 col : 12 mat θ.a.cr t.4 temp.4 time.4 θ.a.cr ainterp : 21 line 41 sys

res.1 res.2 res.3 res.4 x θ.g x t.init t.final lele / 51 sys

600 t.1 735 t.2 900 t.3 650 t.4 41 mat 24.4 35.8 54.7 81.9 41 mat

res.1 res.2 res.3 res.4 x θ.g x t.init t.final lele / 5 1 sys

View the DE piecewise

t.init 0 : t.12 24.4 : t.23 35.8 : t.34 54.7 : t.final 120.7 : 51 line

res_1 20 t.init t.12 122 t θ.a D.1 dn_GearsBDF : res_2 600 t.12 t.23 114 t θ.a D.2 dn_GearsBDF : res_3 735 t.23 t.34 189 t θ.a D.3 dn_GearsBDF : res_4 900 t.34 t.final 66 t θ.a D.4 dn_GearsBDF : 41 sys

res_2 res_2 2 res_2 rows 12 submatrix : res_3 res_3 2 res_3 rows 12 submatrix : res_4 res_4 2 res_4 rows 12 submatrix : global res_1 res_2 res_3 res_4 stack : Global global 1 col global 2 col augment : 51 line

Global 020 0.2 20.75 0.4 22.41 0.6 24.63 0.8 27.25 1 30.19 1.2 33.39 1.4 36.82 1.6 40.44 1.8 44.23 2 48.17 2.2 52.24 2.4 56.44 2.6 60.75 2.8 65.16 3 69.65 3.2 74.24 3.4 78.9 3.6 83.63 3.8 88.42 202 mat

View the project "Global synthetic"

Global x θ.g x t.init t.final lele / 2 1 sys

x f global 1 col global 2 col x ainterp :

Low step High x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct eval : for U f augment 31 line :

recast for regular tabulation New 0 0.25 120 x f inc :

New 020 0.25 21.08 0.5 23.47 0.75 26.56 1 30.19 1.25 34.23 1.5 38.61 1.75 43.27 2 48.17 2.25 53.28 2.5 58.58 2.75 64.04 3 69.65 3.25 75.4 3.5 81.25 3.75 87.22 162 mat

New x θ.g x t.init t.final lele / 2 1 sys

root is live in Smath . . . undocumented

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t θ 203458 t * 1 + log10 * + :

t Wr 203458 t * 1 + log10 * + :

0.25 θ 184.6

w sol t Wr w - t root : 546918 t * + log10 * + (* w - t root

w sol 546918 t * + log10 * + (* w - t root

copy/paste the RHS of sol(w) ... in argument(w,t) w t argument 546918 t * + log10 * + (* w - :

Solving for (t), given (w)... Roots(range) => 0,t,0,120 w t Sol w t argument 0 ≡ t 0120 solve :

user units time 1 : laps 1 : 21 sys

given 640 :

what is 't' that gives '640' on the red curve time given t Sol (: time 7.7

sanity check time θ 640

DE x f given - 0 ≡ x 0120 solve : laps 26.7

given x θ x t.init t.final lele / time 1000 time 100 - 2 2 mat New DE 1000 DE 100 - 2 2 mat 5 1 sys

given time DE 31 mat 640 7.7 26.7 31 mat

given x θ time 1000 time 100 - 2 2 mat New DE 1000 DE 100 - 2 2 mat 5 1 sys

given x θ time 1000 time 100 - 22 mat New DE 1000 DE 100 - 22 mat 51 sys

The dual discrete solver/inverser. f L H N Lo Hi solve Lo/Hi are the range of the solver ω 0 : W 0 : DE 0 : 13 mat refresh solver before use ≡ dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range W j el ω j el t argument 0 ≡ t Lo Hi solve eval : DE j el x f ω j el - 0 ≡ x Lo Hi solve eval : 21 line for ω W DE augment 61 line :

Ω f 1001000450120 solve :

each solution can be splined for interpolation

Ω 1 col Ω 2 col augment Ω 1 col Ω 3 col augment 2 1 sys

Ω 100 0.1 4.3 120 0.1 5.1 140 0.2 5.8 160 0.2 6.6 180 0.2 7.3 200 0.3 8.1 220 0.3 8.8 240 0.4 9.5 260 0.5 10.2 280 0.6 11300 0.7 11.7 320 0.8 12.4 340 0.9 13.2 360 1.1 13.9 143 mat