<p> NOTES maple "root/argument" </p>

69fb2a9c-e78b-4937-803f-28f5c7c01acc 44 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

t0 1 time :

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

each segment is correct individually. For stacking, they
create duplicates at the junctions ... must be stripped. res_1 20 t.init t.12 50 t θ.a D.1 dn_GearsBDF : res_2 600 t.12 t.23 20 t θ.a D.2 dn_GearsBDF : res_3 735 t.23 t.34 40 t θ.a D.3 dn_GearsBDF : res_4 900 t.34 t.final 122 t θ.a D.4 dn_GearsBDF : 41 sys

1 time t0 - 1.2 s *

strip duplicates ... collect cleaned solutions 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

plot res_1 res_2 res_3 res_4 x θ.g x t.init t.final lele / 51 sys :

OBSERVE: This setup plots mixed scalar θ(x) & discrete suite res_'

1.12 sec 122114 + 189 + 66 + 491

1 sec 5020 + 40 + 66 + 176

piecewise DE after stripping duplicates

plot

stripped duplicates Global 020 0.49 23.33 0.98 29.83 1.46 37.96 1.95 47.21 2.44 57.29 2.93 68.03 3.42 79.27 3.9 90.94 4.39 102.95 102 mat

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 21.31 0.5 23.45 0.75 26.47 1 30.2 1.25 34.24 1.5 38.61 1.75 43.27 2 48.17 2.25 53.28 2.5 58.59 2.75 64.04 3 69.66 3.25 75.39 3.5 81.26 3.75 87.22 162 mat

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

t Wr 203458 t * 1 + log10 * + :

The dual discrete solver/inverser ... accumulates 'N' solutions for further spline f L H N Lo Hi solve Lo/Hi => common range of the solvers 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 t Wr ω j el - 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 :

t0 1 time :

Ω f 1001000450100 solve :

Ω 11 mat 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 13.9 380 1.3 14.7 400 1.5 15.4 420 1.7 16.2 440 1.9 17460 2.2 17.8 480 2.6 18.6 5003 19.5 520 3.4 20.4 540 3.9 21.3 560 4.5 22.3 580 5.1 23.3 600 5.9 24.4 620 6.7 25.5 640 7.7 26.7 660 8.8 28680 10.1 29.4 700 11.6 31720 13.2 33740 15.1 37.2 760 17.3 40780 19.8 41.8 800 22.7 43.5 820 25.9 45.2 840 29.6 47.1 860 33.9 49.2 880 38.7 51.6 900 44.3 54.7 920 50.6 58.8 940 57.9 64.3 960 66.2 71.6 980 75.6 80.5 453 mat 11 mat

each solution can be splined for interpolation

Ω 1 col Ω 2 col augment Ω 1 col Ω 3 col augment 100 20 100 20 - 2 2 mat 3 1 sys

1 time t0 - 119.7 s *

user on-line solve

user on-line  ω ≥ 100 ω 100 :

W t Wr ω - 0 ≡ t 0100 solve eval : DE x f ω - 0 ≡ x 0100 solve eval : 21 line

ω W DE 21 mat 12 mat 100 0.09 4.27 21 mat 12 mat

user on-line  ω ≤ 100 ω 25 :

W t Wr ω - 0 ≡ t 05 solve eval : DE x f ω - 0 ≡ x 05 solve eval : 21 line

ω W DE 21 mat 12 mat 25 0.004 0.637 21 mat 12 mat

Plot/solve on canvas ... copy/paste in blank sheet

<p> NOTES maple "root/argument" </p>

t θ 203458 t * 1 + log10 * + :

x θ

0 θ 20

X 20 :

t θ X - 0 ≡ t 01 solve 0.000000000000000

t0 1 time :

x sol t θ x - 0 ≡ t 0100 solve 20 x ≤ (x 1000 ≤ (& cases :

x sol

1 time t0 - 21 s *

root is live in Smath . . . undocumented

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t Wr 203458 t * 1 + log10 * + :

w sol t Wr 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, 5
............................  Roots(range) => 0,t,0,100 w t Sol w t argument 0 ≡ t 05 solve :

given 50 :

what is 't' that gives '640' on the red curve solution given t Sol (: 0.0277

t0 1 time :

x sol x t argument 0 ≡ t 0100 solve 20 x ≤ (x 1000 ≤ (& cases :

x sol

1 time t0 - 21 s *