Bohmian mechanics is an alternate formalism of quantum mechanics that posits a particle is always existent, and furthermore there is a separate entity describing a wave-like disturbance in space and time, governed by the Schrodinger equation, that affects the motion of particles through a quantum potential energy. While conceptually palatable, in applications Bohmian mechanics presents notable problems of stability and feasibility when it comes to numerical modeling of multiple particles. After demonstrating basic properties of a Bohmian trajectory for a single particle from an exact model, the approximation scheme developed by Oriols and co-workers is generalized and implemented for two and three particles in a two-dimensional harmonic confining potential well. The original approximation scheme involves a set of coupled Schrodinger equations, one per particle associated with a conditional wavefunction. This separation approach tremendously reduces the computational complexity. Unlike mean field theory typically used in multiple particle systems, the lowest level of this approximation scheme retains space-time correlations between particle motions. Here, this separation approach is extended to generalized coordinates. Consequently, particle dynamics is described by a set of separate conditional wavefunctions, where each conditional wavefunction is associated with a generalized coordinate and its non-commuting conjugate momentum. Correlations in time and space are calculated through a set of p coupled one-dimensional Schrodinger equations for p degrees of freedom in the system. Bohmian trajectories are feasibly calculated with far more practicality as demonstrated with two and three interacting particles.