#!/Applications/Julia-1.8.app/Contents/Resources/julia/bin/julia using Plots # for plotting trajectory using DifferentialEquations # for solving ODEs g = 9.8 # acceleration of gravity in m/s^2 t_final = 1.0 # final time of trajectory p = 0.0 # parameters (not used here) function tendency!(dyv::Vector{Float64}, yv::Vector{Float64}, p, t::Float64) # ! notation tells us that arguments will be modified y = yv[1] # 2D phase space; use vcat(x, v) to combine 2 vectors v = yv[2] # dy/dt = v a = -g # dv/dt = -g dyv[1] = v dyv[2] = a end y0 = 10.0 # initial position in meters v0 = 0.0 # initial velocity in m/s yv0 = [y0, v0] # initial condition in phase space tspan = (0.0, t_final) # span of time to simulate prob = ODEProblem(tendency!, yv0, tspan, p) # specify ODE sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8) # solve using Tsit5 algorithm to specified accuracy println("\n\t Results") println("final time = ", sol.t[end]) println("y = ", sol[1, end], " and v = ", sol[2, end]) println("exact v = ", v0 - g * t_final) println("exact y = ", y0 + v0 * t_final - 0.5 * g * t_final^2.0) plot(sol, idxs = (1)) # plot position as a function of time