1 files changed, 173 insertions, 0 deletions
diff --git a/t/disp.jl b/t/disp.jl
new file mode 100644
index 0000000..41ee2bb
--- /dev/null
+++ b/t/disp.jl
@@ -0,0 +1,173 @@
+function calculate_force(
+	left_pos,
+	middle_pos,
+	right_pos,
+	K,
+	alpha = 0,
+	beta = 0,
+)
+	linear_force = K * (middle_pos - left_pos + middle_pos - right_pos)
+	quadratic_force = alpha * (middle_pos - left_pos)^2 + alpha * (middle_pos - right_pos)^2
+	cubic_force = beta * (middle_pos - left_pos)^3 + beta * (middle_pos - right_pos)^3
+	return linear_force + quadratic_force + cubic_force
+end
+
+function tendency!(du, u, p, t)
+	# unpack the params
+	N, K, m = p
+
+	# get the positions and momenta
+	qs = u[1:2:end]
+	ps = u[2:2:end]
+
+	# go over the points in the lattice and update the state
+	for i in 2:N-1
+		mass = m
+		if i == 2 * Int(N / 2) - 1 || i == 2 * Int(N / 2)
+			mass = 10000
+		end
+
+		du[i*2-1] = ps[i] / mass
+		force =
+			du[i*2] = force / mass
+	end
+
+	force_end = K * (qs[2] - 2 * qs[1] + qs[N-1])
+	du[1] = ps[1] / m
+	du[2] = force_end / m
+	du[end-1] = ps[end] / m
+	du[end] = force_end / m
+end
+
+function get_initial_state(
+	N,
+	initial_displacement = 2,
+	initial_velocity = 0,
+)
+	state = zeros(2 * N)
+
+	middle_index = 2 * Int(N / 2) - 1 # middle mass
+	state[middle_index] = initial_displacement
+	state[middle_index+1] = initial_velocity
+	return state
+end
+
+using DifferentialEquations
+function run_simulation(
+	N,
+	K,
+	m,
+	final_time,
+	initial_displacement = 2,
+	initial_velocity = 0,
+)
+	println("Running simulation with N = $N, K = $K, m = $m, final_time = $final_time, initial_displacement = $initial_displacement, initial_velocity = $initial_velocity\n")
+	s_0 = get_initial_state(N, initial_displacement, initial_velocity)
+
+	# pack the params
+	p = N, K, m
+	t_span = (0.0, final_time)
+	prob = ODEProblem(tendency!, s_0, t_span, p)
+	sol = solve(prob, Tsit5(), reltol = 1e-10, abstol = 1e-10) # control simulation
+
+	println("Done Running Sim!\n\n")
+	return sol
+end
+
+using Plots
+function animate_positions(
+	states,
+	time_steps,
+	time_min = 0,
+	time_max = 30,
+	red_threshold = 2,
+)
+	println("Animating positions")
+	anim = @animate for i in 1:length(time_steps)
+		t = time_steps[i]
+		if t < time_min
+			continue
+		end
+		if t > time_max
+			break
+		end
+		positions = states[i][1:2:end]
+		v_middle = states[i][Int(length(states[1]) / 2)]
+		# plot(positions, label = "t = $(round(t, digits = 3)), v_middle=$(round(v_middle, digits=3))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = (-3, 3))
+		if v_middle >= red_threshold
+			plot(positions, label = "t = $(round(t, digits = 3)), v_middle=$(round(v_middle, digits=3))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = (-3, 3),
+				color = :red, legend = :topright,
+			)
+		else
+			plot(positions, label = "t = $(round(t, digits = 3)), v_middle=$(round(v_middle, digits=3))", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", ylim = (-3, 3),
+				color = :blue, legend = :topright,
+			)
+		end
+	end
+	mp4(anim, "t/animate-positions.mp4", fps = 30)
+	println("Done animating positions")
+end
+
+function plot_starting_and_final_positions(
+	states,
+	time_steps,
+)
+	p1 = plot(states[1][1:2:end], label = "Initial", marker = :circle, xlabel = "Mass Number", ylabel = "Displacement", title = "First Three Modes")
+	plot!(p1, states[end][1:2:end], label = "Final", marker = :circle)
+
+	# plot the vels
+	p2 = plot(states[1][2:2:end], label = "Initial", marker = :circle, xlabel = "Mass Number", ylabel = "Velocity", title = "First Three Modes")
+	plot!(p2, states[end][2:2:end], label = "Final", marker = :circle)
+
+	# save the plots
+	savefig(p1, "t/initial-final-positions.png")
+	savefig(p2, "t/initial-final-velocities.png")
+end
+
+function analyize_vels(
+	states,
+	time_steps,
+	threshold = 1.975,
+)
+	println("Analyzing velocities:\n")
+	output = []
+	for i in 1:length(states)
+		if states[i][Int(length(states[i]) / 2)] >= threshold
+			push!(output, i)
+			println("Time: ", time_steps[i], " Position: ", states[i][Int(length(states[i]) / 2)])
+		end
+	end
+
+	# plot the first 10 seconds of Velocity
+	data = []
+	for i in 1:length(states)
+		if time_steps[i] > 10
+			break
+		end
+		push!(data, states[i][Int(length(states[i]) / 2)])
+	end
+	p = plot(data, label = "Velocity Over Time", xlabel = "Time", ylabel = "Velocity")
+	savefig(p, "t/velocity-over-time.png")
+
+	println("\nDone!\n\n")
+	return output
+end
+
+# Run the simulation
+N = 10 # number of masses
+beta = 0 # cubic string spring
+K = 100 # spring constant
+A = 10 # amplitude
+final_time = 10000 # seconds
+m = 1 # mass of particles
+plot_data = []
+
+my_vel = 10
+
+sol = run_simulation(N, K, m, final_time, 0, my_vel)
+
+println("final time: ", sol.t[end])
+# s = sol.u[1:2:end]
+analyize_vels(sol.u, sol.t, my_vel)
+plot_starting_and_final_positions(sol.u, sol.t)
+animate_positions(sol.u, sol.t, 0, 1, my_vel)