  We introduce continuous Lagrangian reachability (CLRT), a new algorithm for
the computation of a tight and continuous-time reachtube for the solution flows
of a nonlinear, time-variant dynamical system. CLRT employs finite strain
theory to determine the deformation of the solution set from time $t_i$ to time
$t_{i+1}$. We have developed simple explicit analytic formulas for the optimal
metric for this deformation; this is superior to prior work, which used
semi-definite programming. CLRT also uses infinitesimal strain theory to derive
an optimal time increment $h_i$ between $t_i$ and $t_{i+1}$, nonlinear
optimization to minimally bloat (i.e., using a minimal radius) the state set at
time $t_i$ such that it includes all the states of the solution flow in the
interval $[t_i,t_{i+1}]$. We use $\delta$-satisfiability to ensure the
correctness of the bloating. Our results on a series of benchmarks show that
CLRT performs favorably compared to state-of-the-art tools such as CAPD in
terms of the continuous reachtube volumes they compute.
