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Diffstat (limited to 'hw3/DrivenPendulum.jl')
| -rw-r--r-- | hw3/DrivenPendulum.jl | 110 |
1 files changed, 0 insertions, 110 deletions
diff --git a/hw3/DrivenPendulum.jl b/hw3/DrivenPendulum.jl deleted file mode 100644 index 53a1af9..0000000 --- a/hw3/DrivenPendulum.jl +++ /dev/null @@ -1,110 +0,0 @@ -#!/Applications/Julia-1.8.app/Contents/Resources/julia/bin/julia - -# Simulate driven pendulum to find chaotic regime - -using Plots # for plotting trajectory -using DifferentialEquations # for solving ODEs - -ω0 = 1.0 # ω0^2 = g/l -β = 0.5 # β = friction -f = 1.2 # forcing amplitude -ω = .66667 # forcing frequency -param = (ω0, β, f, ω) # parameters of anharmonic oscillator - -function tendency!(dθp::Vector{Float64}, θp::Vector{Float64}, param, t::Float64) - - (θ, p) = θp # 2d phase space - (dθ, dp) = dθp # 2d phase space derviatives - - (ω0, β, f, ω) = param - - a = -ω0^2 * sin(θ) - β * dθ + f * forcing(t, ω) # acceleration with m = 1 - - dθp[1] = p - dθp[2] = a -end - -function forcing(t::Float64, ω::Float64) - - return sin(ω * t) - -end - -function energy(θp::Vector{Float64}, param) - - (θ, p) = θp - - (ω0, β, f, ω) = param - - pe = ω0^2 * (1.0 - cos(θ)) - ke = 0.5 * p^2 - - return pe + ke - -end - -# take a list and reduce theta to the interval [-π, π] -function clean_θ(θ::Vector{Float64}) - rθ = [] - for i in 1:length(θ) - tmp = θ[i] % (2 * π) - if tmp > π - tmp = tmp - 2 * π - elseif tmp < -π - tmp = tmp + 2 * π - end - push!(rθ, tmp) - end - return rθ -end - -function get_poincare_sections(sample_θ, sample_p, sample_t, Ω_d, ϵ::Float64, phase_shift=0.0::Float64) - n = 0 - - poincare_θ = [] - poincare_p = [] - - for i in 1:length(sample_θ) - if abs(sample_t[i] * Ω_d - (2 * π * n + phase_shift)) < ϵ / 2 - push!(poincare_θ, sample_θ[i]) - push!(poincare_p, sample_p[i]) - n += 1 - end - end - - return (poincare_θ, poincare_p) -end - -θ0 = 0.2 # initial position in meters -p0 = 0.0 # initial velocity in m/s -θp0 = [θ0, p0] # initial condition in phase space -t_final = 1000.0 # final time of simulation - -tspan = (0.0, t_final) # span of time to simulate - -prob = ODEProblem(tendency!, θp0, tspan, param) # specify ODE -sol = solve(prob, Tsit5(), reltol=1e-12, abstol=1e-12) # solve using Tsit5 algorithm to specified accuracy - -sample_times = sol.t -println("\n\t Results") -println("final time = ", sample_times[end]) -println("Initial energy = ", energy(sol[:,1], param)) -println("Final energy = ", energy(sol[:, end], param)) - -(ω0, β, f, ω) = param - -# Plot of position vs. time -# θt = plot(sample_times, [sol[1, :], f * forcing.(sample_times, ω)], xlabel = "t", ylabel = "θ(t)", legend = false, title = "θ vs. t") - -# Phase space plot -cleaned = clean_θ(sol[1, :]) -θp = scatter(cleaned, sol[2, :], xlabel = "θ (radians)", ylabel = "ω (radians/s)", legend = false, title = "Phase Space Plot", mc=:black, ms=.35, ma=1) - - -# plot the poincare sections -(poincare_θ, pointcare_p) = get_poincare_sections(cleaned, sol[2, :], sol.t, ω, 0.1) -s1 = scatter(poincare_θ, pointcare_p, xlabel = "θ (radians)", ylabel = "ω (radians/s)", label="2nπ", title = "Poincare Sections", mc=:red, ms=2, ma=0.75) -s2 = scatter(get_poincare_sections(cleaned, sol[2, :], sol.t, ω, 0.1, π / 2.0), mc=:blue, ms=2, ma=0.75, label="2nπ + π/2", title="Poincare Sections", xlabel = "θ (radians)", ylabel = "ω (radians/s)", legend=:bottomleft) -s3 = scatter(get_poincare_sections(cleaned, sol[2, :], sol.t, ω, 0.1, π / 4.0), mc=:green, ms=2, ma=0.75, label="2nπ + π/4", title="Poincare Sections", xlabel = "θ (radians)", ylabel = "ω (radians/s)") - -plot(θp, s1, s2, s3)
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