Bird flies in circle, using cosine and sine. Spacebar hides diagrams and makes flight smooth without pauses. Y radius proportion scales the Y position. Diagram shows X position as distance from center, computed as cosine θ of the angle multiplied by the radius.
Diagram shows bird's X position varies with cosine of angle multiplied by the max radius length (150). Y position also computed with trig, but multiplied by the Y proportion slider variable. With Y proportion very low, circling is in Z axis. With Y proportion set to 1, circling is in all axes. Bird rotation and flapping rendered in Blender, modified from an existing model.