From a24f7a5cef19b666b1a6085b655069341ba8f450 Mon Sep 17 00:00:00 2001 From: Permondes Date: Mon, 5 Feb 2024 19:11:30 +0100 Subject: [PATCH] Comet on parabolic orbit; root, diodes Applications: Comet on parabolic orbit Technical: - Intro to solving differential equations and integrals - Added root-calculation - Details about diodes and Z-diodes AESL: Ports for diodes and z-diodes --- AESL/TP1 05.15 Comet.AESL | 53 +++++++++++++++++++++++++ Analog Engine Example Applications.odt | Bin 7389772 -> 1243880 bytes Analog Engine Scripting Language.odt | Bin 45561 -> 39838 bytes Analog Engine Technical Topics.odt | Bin 70992 -> 303478 bytes 4 files changed, 53 insertions(+) create mode 100644 AESL/TP1 05.15 Comet.AESL diff --git a/AESL/TP1 05.15 Comet.AESL b/AESL/TP1 05.15 Comet.AESL new file mode 100644 index 0000000..fc83617 --- /dev/null +++ b/AESL/TP1 05.15 Comet.AESL @@ -0,0 +1,53 @@ +IDENTIFICATION DIVISION +PROGRAM-ID Comet +VERSION 20240205 +COMMENT A comet moves on a parabolic orbit in the gravitational field of the stationary sun. +COMMENT Its orbital plane coincides with the plane of the Earth's orbit, which is assumed to be circular. +COMMENT The perihelion distance is one third of the Earth's orbital radius R.E. +COMMENT How long does the comet move within the Earth's orbit? +COMMENT t(r)=root(2/(gamma*m(sun))*integral from 1/3RE to RE (r/root(r-1/3 RE)) dr + +ENVIRONMENT DIVISION +ENGINE Anabrid-THAT +TIMEBASE 100ms # use SLOW on both integrators +REQUIRES COEFFICIENT 3, INTEGRATOR 2, COMPARATOR 1, SUMMER 1, OPEN-AMP 2, MULTIPLIER 2, INVERTER 1 + +DATA DIVISION +OUTPUT OUTPUT.X -xlimited +OUTPUT OUTPUT.Y result +COEFFICIENT.1 Factor # root(2/(gamma*m)), scaled to 0,142 10kd/Tm^3/2 +COEFFICIENT.2 RE # Earth's orbital radius, scaled to 0,150 Tm +COEFFICIENT.3 1/3RE # note: dependent on RE, scaled to 0,05 Tm + +PROGRAM DIVISION ++1 -> COEFFICIENT.RE -> RE ++1 -> COEFFICIENT.1/3RE -> 1/3RE + +# obtaining x through integration of 1, starting at 1/3RE ++1, IC:1/3RE -> INTEGRATOR -> -x + +# limiting x to the upper limit of the integral RE and set x=0 if beyond +A:-x, B:RE, GT0:-x -> COMPARATOR -> -xlimited + +-xlimited, 1/3RE -> SUMMER -> -(-x+1/3RE)=x-1/3RE + +# root of x-1/3RE +## first invert because the input of a root has to be negative +x-1/3RE -> INVERTER -> -(x-1/3RE) +## now make sure the input is never >0 (which causes the circuit to error) +A:-(x-1/3RE), LT0:-(x-1/3RE) -> COMPARATOR -> -(x-1/3RE)limited +## now calculate the root +-(x-1/3RE)limited, OA1 -> OPEN-AMP -> root +root, root -> MULTIPLIER -> OA1 + +# x/root +-xlimited, OA2 -> OPEN-AMP -> x/root +x/root, root -> MULTIPLIER -> OA2 + +# integral +x/root -> INTEGRATOR -> integral +integral -> COEFFICIENT.Factor -> result + +OPERATION DIVISION +MODE REPEAT +OP-TIME 111ms diff --git a/Analog Engine Example Applications.odt b/Analog Engine Example Applications.odt index ec40f5f15a330f070a4b8bb4877d577834074722..94495eed9fcd2fbe410fa6be83762e22bd57381c 100644 GIT binary patch delta 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