879759d6-589d-430f-85e6-9f9060380552 9 Валерий Очков 4 5 false false 0 7 decimal

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

m 1 :

r.o 20 m * :

α 60 ° * :

x.c0 r.o 90 ° * - α 2 / + cos * : 10 m *

y.c0 r.o 90 ° * - α 2 / + sin * : 17.32 m * -

x.cp0 10 m * - :

y.cp0 20 m * - :

Guess values

a1 0.1 m * :

b1 7.5 m * :

x a b y a x x.cp0 - b / (3^(* y.cp0 + :

https://en.wikipedia.org/wiki/Track_transition_curve

Α 90 ° * - α 2 / + ( 270 ° * α 2 / - ( 90 ° * - α 2 / + 1 ° * + ( range : r.o Α cos vectorize * r.o Α sin vectorize * augment 2 1 line x.cp0 y.cp0 . 3 black 1 5 mat x.c0 y.c0 . 3 black 1 5 mat X x.cp0 x.c0 x.cp0 0.01 m * + range : X X a1 b1 y vectorize augment 2 1 line 4 1 sys

x a b κ x a b y x 2 diff abs 1 x a b y x diff 2^+ sqrt 3^/ :

https://en.wikipedia.org/wiki/Curvature

x.c0 a1 b1 y m 18.1 -

y.c0 m 17.32 -

x.c0 a1 b1 κ m 1 -^0.02531

1 r.o / m 1 -^0.05

x.c0 a# b# y y.c0 - x.c0 a# b# κ 1 r.o / - 21 mat a1 b1 21 mat 105 -^mm * 105 -^mm * 21 mat FindRoot #

x.c0 a b y y.c0 ≡ x.c0 a b κ 1 r.o / ≡ 21 mat a b 21 mat a1 b1 21 mat roots #

x# a# b# F x.c0 a# b# y y.c0 - x.c0 a# b# κ 1 r.o / - 21 mat :

a b f.1 x.c0 a b y y.c0 - :

a b f.2 x.c0 a b r r.o - :

v f v 1 el m * v 2 el m * v 3 el m * F :

step 0 :

a b F a b f.1 a b f.2 21 mat :

guess x.c0 a1 b1 13 mat transpose m 1 -^* :

eps 1010 -^:

a b J a b f.1 a diff a b f.1 b diff a b f.2 a diff a b f.2 b diff 22 mat :

null a b 31 mat guess step eps XX f al_nleqsolve m * :

a m 0.1411

GV Newton a b 21 mat GV : a b f.1 a b f.2 ≉ a b 21 mat a b 21 mat a b J (1 -^a b F * - : 11 line while 11 line a b 21 mat 31 line :

b 7.4963 m *

x.c0 a b y y.c0 - mm 0.1249

x.c0 a b κ 1 r.o / - 1 m / 0.0179 -

a1 b1 21 mat Newton 0.1 7.5 21 mat