From: Permondes Date: Wed, 11 Dec 2024 15:45:37 +0000 (+0100) Subject: Potentials and Motion X-Git-Url: https://permondes.de/gitweb/Analog_Engine.git/commitdiff_plain/refs/heads/main Potentials and Motion Separated physics of potentials into “Potentials and Motion” Applications: - Harmonic oscillator with gravity - Pendulum with 4th order Taylor approximation --- diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index 0a43759..6152e06 100644 Binary files a/Analog Engine Example Applications.odt and b/Analog Engine Example Applications.odt differ diff --git a/Potentials and Motion.odt b/Potentials and Motion.odt new file mode 100755 index 0000000..cf28c35 Binary files /dev/null and b/Potentials and Motion.odt differ diff --git a/scripts/Pendulum.LACE b/scripts/Pendulum.LACE new file mode 100644 index 0000000..c5e8ab2 --- /dev/null +++ b/scripts/Pendulum.LACE @@ -0,0 +1,37 @@ +# Pendulum: Comparing Harmonic Oscillator with 4th order Taylor approximation + +### Taylor 4 approximation: phi'' = - g/r * (phi - 1/6 * phi^3) +# fortunately, the components of orders 0, 2 and 4 are zero + +coefficient.1 -> g/r +coefficient.2 -> 1/6 # set to 0,167 or 0 (for harmonic solution) +coefficient.3(-1) -> -phi0 + +iintegrate phi'' -> -phi' +iintegrate -phi' -> phi + IC: -phi0 + +multiply phi, phi -> phi^2 +multiply phi^2, phi -> phi^3 +invert phi^3 -> -phi^3 + +cmultiply 1/6, -phi^3 -> -1/6*phi^3 +isum phi, -1/6*phi^3 -> -(phi-1/6*phi^3) +cmultiply -(phi-1/6*phi^3), g/r -> -g/r*(phi-1/6*phi^3) +assign -g/r*(phi-1/6*phi^3) -> phi'' + +output phi -> out.x + +### Harmonic oscillator: phi'' = - g/r * phi +coefficient.5 -> g/r_h # identical to g/r +coefficient.7(-1) -> -phi0_h # identical to -phi0 + +iintegrate phi_h'' -> -phi_h' +iintegrate -phi_h' -> phi_h + IC: -phi0_h +invert phi_h -> -phi_h + +cmultiply -phi_h, g/r_h -> -g/r*phi_h +assign -g/r*phi_h -> phi_h'' + +output phi_h -> out.y diff --git a/scripts/TP1 04.12 Harmonic Oscillator.LACE b/scripts/TP1 04.12 Harmonic Oscillator.LACE new file mode 100644 index 0000000..89b0723 --- /dev/null +++ b/scripts/TP1 04.12 Harmonic Oscillator.LACE @@ -0,0 +1,31 @@ +# Harmonic Oscillator +# A mass m is subject to a force F=-k*r. +# What is the trajectory if the mass starts at position (a,0,0)? +# How much time does it take to pass through zero? +# What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)? +# Compare to the case including gravity on earth in x direction +# m*x'' = -k*x + g +# m*y'' = -k*y (z can be set to 0). + +coefficient.1(-1) -> -a # (a,0,0), has to be negative because x' is negative +coefficient.2 -> k/m_x # k/m for x +coefficient.3(+1) -> v0 # (0,v0,0), has to be positive because y'' is positive +coefficient.4 -> k/m_y # k/m for y, identical to k/m for x +coefficient.5(-1) -> -g # g + +iintegrate x'' -> -x' +iintegrate -x' -> x + IC: -a +cmultiply (k/m_x, x) -> k/m*x +isum (k/m*x, -g) -> -k/m*x+g +assign (-k/m*x+g) -> x'' + +iintegrate y'' -> -y' + IC: v0 +iintegrate -y' -> y +cmultiply (k/m_y, y) -> k/m*y +invert (k/m*y) -> -k/m*y +assign (-k/m*y) -> y'' + +output x -> out.x +output.y -> out.y diff --git a/scripts/TP1 07.19 Falling Mass.SALSA b/scripts/TP1 07.19 Falling Mass.SALSA deleted file mode 100644 index 3f3dc6b..0000000 --- a/scripts/TP1 07.19 Falling Mass.SALSA +++ /dev/null @@ -1,55 +0,0 @@ -# Wiring mache ich von links nach rechts !!! - -...IDENTIFICATION DIVISION -...PROGRAM-ID FallingParticle -...VERSION 20240225 -...COMMENT Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h. -...COMMENT Differential Equations: -...COMMENT x''=-bz'+ay' # x-axis is along latitude, directed to east -...COMMENT y''=-ax' # y-axis is along longitude, directed to north -...COMMENT z''=-g+ax' # z-axis is perpendicular to the surface of earth -...COMMENT g: gravitational acceleration = 9,81 m/s² -...COMMENT a: 2*omega*sin(phi) -...COMMENT b: 2*omega*cos(phi) -...COMMENT omega: rotation velocity of the earth = 2*pi/day -...COMMENT phi: Latitude of location (0-90°) -...COMMENT Initial Condition: z(0)=h -...COMMENT The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*). -...COMMENT It could also be solved in a separated algorithm omitting x. - -...ENVIRONMENT DIVISION -...TIMEBASE 1ms - -...DATA DIVISION -SET COEFFICIENT.1 TO AY # 2*2pi/day*sin(phi) -SET COEFFICIENT.2 TO AX # = AY -SET COEFFICIENT.3 TO B # 2*2pi/day*cos(phi) -SET COEFFICIENT.4 TO G # gravitational acceleration = 9,81 m/s² -SET COEFFICIENT.5 TO H # height h -SET OUTPUT.X TO x -SET OUTPUT.Y TO y -SET OUTPUT.Z TO z - -INITIALIZE H by -1 TO -h # same as COMPUTE -1 TIMES H TO -h -INITIALIZE G by +1 TO g - -INTEGRATE 1*-bz',1*ay' TO -x' # Input is x'' -INTEGRATE -x' TO x - -INTEGRATE y'' TO -y' -INTEGRATE -y' TO y - -INTEGRATE z'' TO -z' -INTEGRATE -z', IC:-h, LIMIT:(z >= 0) TO z - --x' * AX -> -ax' --ax' = y'' --y' * AY -> -ay' -INVERT -ay' TO ay' --z' * B -> -bz' -ADD 1*-ax', 1*g TO -g+ax' --g+ax' = z'' - -...OPERATION DIVISION -...MODE REPEAT -...OP-TIME 7,3ms