"Julia runs on the beach."
Translation:Julia läuft am Strand.
The distinction is not action/motion versus rest, but rather whether the place is the destination of motion or just a location.
Here, the beach is not a destination: she runs on the beach the whole time, rather than running to the beach from somewhere else. The beach is the location where her running takes place.
Sie läuft an den Strand would mean that she runs to or onto the beach from somewhere else.