span class="math inline">\(L\)</span> leapfrog steps, a total of <span class="math inline">\(L \, \epsilon\)</span> time is
simulated. The resulting state at the end of the simulation (<span class="math inline">\(L\)</span>
repetitions of the above three steps) will be denoted
<span class="math inline">\((\rho^{*}, \theta^{*})\)</span>.</p>
<p>The leapfrog integrator’s error is on the order of <span class="math inline">\(\epsilon^3\)</span> per
step and <span class="math inline">\(\epsilon^2\)</span> glob