Although the Finite Element Method (FEM) [1] is at the basis of most civil engineering studies, in some cases structures are subject to so much deformations that a more robust approach is necessary. For instance, the Material Point Method (MPM) [2] avoids mesh distortion issues by fixing the mesh and letting the integration points (i.e. material points) move freely within. This hybrid Eulerian-Lagrangian formulation requires the velocity field to be frequently transported between grid points and integration points, as part of the motion integration procedure. The latter being assured by different strategies (e.g. PIC, FLIP, APIC), a particular attention has to be given to their capacity to conserve the energy. This study investigates the impact of the motion integration strategy on the energy conservation in MPM. A formulation of each strategy is first given, and several of them are then tested in two basic cases where a simple cubic body is simulated. The first one considers the body to fall under gravity and deform upon impact on the floor, involving only a translational motion. The results show that PIC-based motion integration strategies dissipate the energy only when the body deforms, while FLIP-based strategies accurately preserve it through each bounce. The second case considers the body to move both in a translational and rotational motion. It is shown that the so called "affine augmentation" procedure, introduced with the APIC strategy [3], is necessary in order to preserve the rotational motion of the cube. Indeed, non-affine augmented strategies completely (or almost, for FLIP-based strategies) lose the body's angular momentum during the first steps, while affine augmented strategies conserves it much better (or totally for the case of affine augmented FLIP-based strategies).