examples: improve the pendulum simulation, with several modes and diagrams (#13446)

examples/pendulum-simulation/modules/sim/sim_test.v

@@ -0,0 +1,64 @@
+module sim
+
+const (
+	sim_test_mock_params = SimParams{
+		rope_length: 0.25
+		bearing_mass: 0.03
+		magnet_spacing: 0.05
+		magnet_height: 0.03
+		magnet_strength: 10
+		gravity: 4.9
+	}
+	sim_test_mock_state = SimState{
+		position: vector(
+			x: -0.016957230930171364
+			y: -0.02937078552673521
+			z: 0.002311063475327252
+		)
+		velocity: vector(
+			x: -7.251158929833104
+			y: -12.559375680227724
+			z: -105.91539687686381
+		)
+		accel: vector(
+			x: -8.337034766251843e-11
+			y: -2.842170943040401e-10
+			z: 1.2126596023639044e-10
+		)
+	}
+)
+
+pub fn test_satisfy_rope_constraint() {
+	mut state := SimState{
+		...sim.sim_test_mock_state
+	}
+
+	state.satisfy_rope_constraint(sim.sim_test_mock_params)
+	assert state.position.x == -0.016957230930171364
+	assert state.position.y == -0.02937078552673521
+	assert state.position.z == 0.002311063475327252
+	assert state.velocity.x == -7.251158929833104
+	assert state.velocity.y == -12.559375680227724
+	assert state.velocity.z == -105.91539687686381
+	assert state.accel.x == -8.337034766251843e-11
+	assert state.accel.y == -2.842170943040401e-10
+	assert state.accel.z == 1.2126596023639044e-10
+}
+
+pub fn test_increment() {
+	mut state := SimState{
+		...sim.sim_test_mock_state
+	}
+
+	delta_t := 0.0005
+	state.increment(delta_t, sim.sim_test_mock_params)
+	assert state.position.x == -0.016957230930171364
+	assert state.position.y == -0.02937078552673524
+	assert state.position.z == 0.0023110634753272796
+	assert state.velocity.x == -7.251158929833044
+	assert state.velocity.y == -12.559375680227637
+	assert state.velocity.z == -105.9153968768638
+	assert state.accel.x == 1.2126596023639044e-10
+	assert state.accel.y == 1.7431981783981126e-10
+	assert state.accel.z == 3.031649005909761e-11
+}