The classic Lagrangian mechanics approach allows for solving virtually any physical problem only for a chosen set of generalized coordinates, thus eliminating unnecessary computations. With certain approximations, this approach yields a system of first-order non-linear ordinary differential equations. Such a system can be solved numerically relatively fast (less than 1 s per run for a single CPU). We show the application of Lagrangian mechanics to problems of asymmetric fracture growth in length due to a lateral confining stress gradient and in height due to vertical confining stress contrasts. In both cases, we build a model and solve model equations. We demonstrate the flexibility of this approach and its potential for creating ultrafast semi-analytical models of hydraulic fracture propagation.

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