Biological organisms have presumably adapted their behaviors or features in response to surrounding mechanical forces or instabilities to achieve better performance. In this talk, I will discuss three problems in which the dynamical system approach elucidates the physics behind animal behaviors. First, we investigated how cats and dogs transport water into the mouth using an inertia-driven (lapping) mechanism. We found that to maximize water intake per lap, both cats and dogs close the jaw at the column break-up time governed by unsteady inertia. This break-up (or pinch-off) time can be predicted using the stability analysis of the water column in which surface tension balances with inertia. Second, we studied how animals plunge-dive and survive impact. Physical experiments using an elastic beam as a model for the body attached to different shapes revealed limits for the stability of the injuries during plunge-dive. The body response can be simplified as the Euler beam buckling problem with unsteady impact force on the diving front. Finally, I will discuss the mechanism of releasing water lodged in the ear canal. For example, people often shake their head sideways to remove water out of ear canal after swimming or showering. This removal process involves high acceleration to push water out of a canal, which is analogous to the Rayleigh-Taylor instability.