First draft of DANCE

[Analog_Engine.git] / AESL / TP1 07.19 Falling Mass.DANCE

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+# FallingParticle, VERSION 20240225
+# Calculate the deflection from the vertical caused by the Earth's rotation of a particle falling freely from rest from a height h.
+# Differential Equations:
+#    x''=-bz'+ay' # x-axis is along latitude,  directed to east
+#    y''=-ax'     # y-axis is along longitude, directed to north
+#    z''=-g+ax'   # z-axis is perpendicular to the surface of earth
+#    g: gravitational acceleration = 9,81 m/s²
+#    a: 2*omega*sin(phi)
+#    b: 2*omega*cos(phi)
+#    omega: rotation velocity of the earth = 2*pi/day
+#    phi: Latitude of location (0-90°)
+#    Initial Condition: z(0)=h
+# The full solution requires 6 INTEGRATORs, Anabrid-THAT just has 5. The deflection to longitude (y) is neglegible and can be omitted (marked #*).
+# It could also be solved in a separated algorithm omitting x.
+
+coefficient(1): a_y
+coefficient(2): a_x
+coefficient(3): b
+coefficient(4): +1 -> g
+coefficient(5): -1 -> -h
+
+iintegrate (-bz', ay') -> -x' # Input is x''
+iintegrate (-x') -> x
+
+iintegrate (y'') -> -y'
+iintegrate (-y') -> y
+
+iintegrate (z'') -> -z'
+iintegrate (-z') -> z:
+   IC: -h
+   limit: GT0 # via z to cathode of diode to SJ 
+   
+-x' * a_x -> -ax'
+y'' = -ax'
+-y' * a_y -> ay'
+invert (-ay') -> ay'
+-z' * b -> -bz'
+isum(-ax', g) -> z'' # gives -g+ax'
+
+# x -> output (x)
+# y -> output (y)
+# z -> output (z)
+
+#OP-TIME 7,3ms