Applications: Longitudinal oscillating chains; PDEs

[Analog_Engine.git] / scripts / TP1 10.30 Linear Molecule.LACE

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+# TP1 10.30 Linear Molecule
+# In a linear molecule of symmetric construction of type A-B-A the atoms are harmonically coupled and are performing small oscillations around the equilibrium positions.
+
+# s1'' = -omega0^2*s1 + omega0^2*s2
+# s2'' = -my (-omega0^2*s1 + omega0^2*s2 + omega0^2*s2 - omega0^2*s3)
+# s3'' = omega0^2*s2 - omega0^2*s3
+
+# NB: all integrators have to run with 100 nF capacitance, i.e. SLOW mode
+
+coefficient(1): omega0^2_1 # omega0^2 for s1
+coefficient(2): omega0^2_2 # omega0^2 for s2 # same as omega0^2_1
+coefficient(3): omega0^2_3 # omega0^2 for s3 # same as omega0^2_1
+coefficient(4): my
+coefficient(5): -1 -> -s1_0 # initial position of s1
+coefficient(6): -1 -> -s3_0 # initial position of s3
+# initial positon of s2, the central mass, is set to 0
+
+iintegrate -omega0^2_1*s1, omega0^2_2*s2 -> -s1'   # input is s1''
+iintegrate -s1' -> s1
+   IC: -s1_0
+invert s1 -> -s1
+-s1 * omega0^2_1 -> -omega0^2_1*s1
+
+iintegrate -my*bracket -> -s2'   # input is s2''
+# the following integrator has to be built up manually as THAT only has 5 integrators and we need 6
+# iintegrate -s2' -> s2
+openamp -s2' -> s2
+  loopback: capacitor(100nF)
+s2 * omega0^2_2 -> omega0^2_2*s2
+isum -omega0^2_1*s1, omega0^2_2*s2, omega0^2_2*s2, -omega0^2_3*s3 -> -bracket
+-bracket * my -> -my*bracket
+
+iintegrate omega0^2_2*s2, -omega0^2_3*s3 -> -s3'   # input is s3''
+iintegrate -s3' -> s3
+  IC: -s3_0
+invert s3 -> -s3
+-s3 * omega0^2_3 -> -omega0^2_3*s3
+
+ output(x): s1
+ output(y): s2
+ output(z): s3