From 5e25727877da020b0b23132fec8c0ea70288a18b Mon Sep 17 00:00:00 2001
From: samuel niederer <samuel.niederer@ost.ch>
Date: Sun, 24 Jul 2022 12:03:25 +0200
Subject: add presentation files

---
 buch/papers/kra/scripts/simulation.py | 40 +++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 buch/papers/kra/scripts/simulation.py

(limited to 'buch/papers/kra/scripts/simulation.py')

diff --git a/buch/papers/kra/scripts/simulation.py b/buch/papers/kra/scripts/simulation.py
new file mode 100644
index 0000000..8bccb6a
--- /dev/null
+++ b/buch/papers/kra/scripts/simulation.py
@@ -0,0 +1,40 @@
+import sympy as sp
+
+
+class Simulation:
+    def __init__(self):
+        self.k_1, self.k_2, self.k_c = sp.symbols("k_1 k_2 k_c")
+        self.m_1, self.m_2 = sp.symbols("m_1 m_2")
+        self.t = sp.symbols("t")
+        K = sp.Matrix(
+            [[-(self.k_1 + self.k_c), self.k_c], [self.k_c, -(self.k_2 + self.k_c)]]
+        )
+        M = sp.Matrix([[1 / self.m_1, 0], [0, 1 / self.m_2]])
+        A = M * K
+
+        self.eigenvecs = []
+        self.eigenvals = []
+        for ev, mult, vecs in A.eigenvects():
+            self.eigenvecs.append(sp.Matrix(vecs))
+            self.eigenvals.extend([ev] * mult)
+
+    def __call__(self, t, x_0, k_1, k_c, k_2, m_1, m_2):
+        params = {
+            self.k_1: k_1,
+            self.k_c: k_c,
+            self.k_2: k_2,
+            self.m_1: m_1,
+            self.m_2: m_2,
+        }
+        x_0 = sp.Matrix(x_0)
+        eig_mat = sp.Matrix.hstack(*self.eigenvecs).subs(params)
+        g = eig_mat.inv() * x_0
+        L = sp.Matrix(
+            [
+                g[0] * sp.cos(self.eigenvals[0].subs(params) * self.t),
+                g[1] * sp.cos(self.eigenvals[1].subs(params) * self.t),
+            ]
+        )
+        x = eig_mat * L
+        f = sp.lambdify(self.t, x, "numpy")
+        return f(t).squeeze()
-- 
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