<content> <p> Functions </p> </content>

57e38a15-0890-4eca-918c-2070a3345b00 32 8 5 false false 0 0 decimal

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

Data

X 28 :

Y 3 :

L1 9 :

L2 6.8 :

L3 9.6 :

L4 13 :

ΔL L2 L3 + :

Δ.23 L2 2^L3 2^- :

S.23 L2 2^L3 2^+ :

uy 0121 mat :

M 2021013 mat :

g 1 :

<content> <p> Functions </p> </content>

Potential energy:

y Vfn g M * y * :

y is a 3x1 vector

Coordinates of masses:

y.1 y.3 xyfn x.1 x.3 21 mat L1 2^y.1 2^- sqrt X L4 2^y.3 Y - (2^- sqrt - 21 mat : Δx.13 Δy.13 21 mat x.3 x.1 - y.3 y.1 - 21 mat : a 4 Δx.13 2^Δy.13 2^+ (* : b 4 Δ.23 Δx.13 2^+ Δy.13 2^+ (* Δy.13 * - : c Δ.23 2^2 S.23 * Δx.13 2^* - 2 Δ.23 * Δy.13 2^* + Δx.13 2^Δy.13 2^+ (2^+ : disc b 2^4 a * c * - : disc 0 > δyp b - disc sqrt + 2 a * / : δyn b - disc sqrt - 2 a * / : δy.12 δyp δyn Max : 31 line disc abs 108 -^< δy.12 b 2 a * / - : δy.12 20 - : if if δx.12 2 Δy.13 * δy.12 * - Δ.23 + Δx.13 2^Δy.13 2^+ + (2 Δx.13 * / : x.2 y.2 21 mat δx.12 δy.12 21 mat x.1 y.1 21 mat + : x.1 y.1 x.2 y.2 x.3 y.3 32 mat 101 line :

xy.123 plotfn 0012 mat xy.123 X Y 12 mat stack 1001 - 22 mat * :

Initial guesses:

y.1 7 :

y.3 11 :

Coordinates:

xy.init y.1 y.3 xyfn :

Positions resulting from initial guesses:

plot1 xy.init plotfn :

plot1

Choose three sets of y1 and y3 and iterate using a very simple approach:

tol 107 -^:

err 1 :

steps 0 :

maxsteps 1000 :

λ 0.05 :

ΔV.ab 0 :

ΔV.ac 0 :

err tol > (steps maxsteps < (& steps steps 1 + : Update y1 and y2 y.1 λ ΔV.ab sign * y.1 + : y.3 λ ΔV.ac sign * y.3 + : Coordinates of the three masses xy.a y.1 y.3 xyfn : repeatflag 1 : repeatflag xy.b y.1 λ + y.3 xyfn : xy.c y.1 y.3 λ + xyfn : Check for unacceptable y2 values xy.b 22 el Y < (xy.c 22 el Y < (| λ λ 2 / : 11 line repeatflag 0 : if 41 line while Potential energies V.a xy.a uy * Vfn 1 el : V.b xy.b uy * Vfn 1 el : V.c xy.c uy * Vfn 1 el : ΔV.ab V.b V.a - : ΔV.ac V.c V.a - : err ΔV.ab abs ΔV.ac abs 21 mat Max : Reduce size of λ λ 0.99 λ * : 171 line while

err 8.4936388 108 -^*

steps 617

SMath final coordinates

Comparable Mathcad values. Note: Mathcad y-values = (18 - SMath) y-values

xy.a 3.089 8.453 9.436 10.895 18.931 12.314 32 mat

3.089 8.453 9.435 10.895 18.93 12.313 32 mat

xy.b 3.089 8.453 9.436 10.894 18.931 12.314 32 mat

xy.c 3.089 8.453 9.436 10.894 18.931 12.314 32 mat

Final positions:

plot1 xy.a plotfn :

plot1