1. Animal movement arises from a complex interaction between an animal and its heterogeneous environment. The large amount of variables involved in that interaction complicates the ecological inference thereof. In order to better understand movement, the myriad of involved variables can be grouped into behavioural, spatial, and temporal components of the movement process (related to the questions of why, where and when to move), which should be addressed simultaneously. 2. We studied the influence of spatial environmental variation on fine-scale movement trajectories of eland antelope, blue wildebeest and plains zebra in a South-African game reserve, in simultaneous consideration with temporal rhythms and behavioural movement modes. 3. We described the animals' movement process as multi-mode random walks using hidden Markov models (HMMs), where both the probabilities of switching between modes as well as the mode-dependent speed and turning angle distributions were a function of time of day, tree cover and terrain slope. 4. The fitted HMMs clustered the trajectories of all three species into a fast and directed "transit" mode and a slow and tortuous "encamped" mode. All movement properties displayed a strong diel pattern, with the effects of tree cover and slope on speed being largest in the evening when animals generally moved faster. Wildebeest and zebra in their transit mode moved faster with increasing tree cover whereas eland moved slower, but only so on steep terrain. In the encamped mode, tree cover had almost no effect on speed, but a strong effect on tortuosity. The animals also generally moved more tortuously with higher tree cover, even more so on sloping terrain. 5. Due to our integrated approach, we showed that the influence of spatial environmental heterogeneity on animal movement varies greatly in diel cycles and between movement modes, reflecting variation in the animals' habitat selection and decision making throughout the day. Thus, focusing on the interactions between why, when and where to move is needed to more truthfully describe and understand animal movement.