Let us put your mind at seas... it's okay to shake your dinos! Dinoflagellates exist in tumultuous environments in the natural world. They're used to cruising with the currents and crashing with the waves, so a little shake is nothing they aren’t well accustomed to.
Furthermore, dinos are a photosynthetic plankton (marine algae). This means they’re much more akin to the grass in your yard than they are to the dog in your yard. Dinoflagellates don’t have brains, nervous systems, pain receptors or anything of the sort.