[petrovitch (OP)]

My schnauzer plays chase around a hillside that surrounds our swimming pool.  I have filmed her making right angle turns and she never loses a step.  It's like watching a motorcycle race.  Dust if flying from her heels and she is running as hard as she can approaching a 90 degree turn.  Expecting her to slow down, she doesn't.  She makes the turn with grace and speed.

I've seen deer make sudden turns without losing speed too.  How can an animal make a 90 degree turn and not lose speed?  No matter how we arrange the gears we have a loss of power, say in an automobile, when we convert the power generated from the transmission 90 degrees in the rear-end to power the drive wheels.  Does my schnauzer understand the laws of physics much better than automobile engineers?

[DoctorBeaver]

Balance, weight-distribution, and where/when the power is applied.

[lyner]

She is light, with good traction (she can't do her trick on a polished floor) and her power /mass ratio is high.
Cars are comparatively rubbish because cornering takes its place in the  list of design priorities - like safety at high speeds. Also, remember, your doggy is only going relatively slowly. Your appreciation of her performance is, understandably, subjective. Bet she would have a problem catching a hare.

[Bored chemist]

I'm not sure about canine musculature and such but I think dogs can push sideways with their feet. Cars don't have a "sideways" gear (usually).

[lyner]

She can lean into corners like a motorbike. In the end, it's a matter of traction. She has to be able to push herself 'into the corner'.
A formula one racing car could go round the whole circuit at, say, 80mph, without changing gear. But, if you can do 200mph on the straight, you have to slow down for a corner so using your gears gives you the best time. I expect even your pooch* has to slow down a bit for a tight corner.

*excuse my over-familiarity!