Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

make tutorial more clear #6

Open
wants to merge 1 commit into
base: main
Choose a base branch
from
Open

make tutorial more clear #6

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
31 changes: 18 additions & 13 deletions script/models/01-classical_physics.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -55,11 +55,12 @@ using OrdinaryDiffEq, Plots

#Constants
const g = 9.81
L = 1.0
const L = 1.0

#Initial Conditions
#Initial conditions
u₀ = [0,π/2]
tspan = (0.0,6.3)
#Integration time
tspan = (0.0,2pi)

#Define the problem
function simplependulum(du,u,p,t)
Expand All @@ -71,24 +72,29 @@ end

#Pass to solvers
prob = ODEProblem(simplependulum, u₀, tspan)
sol = solve(prob,Tsit5())
sol = solve(prob, Tsit5())

#Plot
plot(sol,linewidth=2,title ="Simple Pendulum Problem", xaxis = "Time", yaxis = "Height", label = ["\\theta" "d\\theta"])
plot(sol, linewidth=2, title="Simple Pendulum Problem", xaxis="Time", yaxis="Height", label=["\\theta" "d\\theta"])


p = plot(sol,vars = (1,2), xlims = (-9,9), title = "Phase Space Plot", xaxis = "Velocity", yaxis = "Position", leg=false)
function phase_plot(prob, u0, p, tspan=2pi)
_prob = ODEProblem(prob.f,u0,(0.0,tspan))
sol = solve(_prob,Vern9()) # Use Vern9 solver for higher accuracy
plot!(p,sol,vars = (1,2), xlims = nothing, ylims = nothing)
plt = plot(sol, vars=(1, 2), xlims=(-9, 9), title="Phase Space Plot", xaxis="Velocity", yaxis="Position", leg=false)
function phase_plot!(plt, prob, u0, T=2pi)
# remake ODEProblem with updated initial conditions
_prob = ODEProblem(simplependulum, u0, (0.0, T))
# solve ODEProblem with updated initial conditions
sol = solve(_prob, Vern9()) # Use Vern9 solver for higher accuracy
# add solution to the plot
plot!(plt, sol, vars=(1, 2))
end
# Loop over initial conditions
for i in -4pi:pi/2:4π
for j in -4pi:pi/2:4π
phase_plot(prob, [j,i], p)
# update Phase Space Plot with new trajectories for different initial conditions
phase_plot!(plt, prob, [j, i])
end
end
plot(p,xlims = (-9,9))
plot(plt, xlims=(-9, 9))


#Double Pendulum Problem
Expand Down Expand Up @@ -261,4 +267,3 @@ plot(sol3.t, energy .- energy[1], title = "Change in Energy over Time", xaxis =

using SciMLTutorials
SciMLTutorials.tutorial_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file])

Loading