top of page

The Mathematics of Gymnastics ~ Gimbal Lock

Updated: Apr 15

Gymnastics is known to be a very mathematical and analytical sport. This comes with pros and cons. The Cons are that kids don’t really understand what acrobatics is all about but the pros are that very dedicated coaches can analyze the theoretically perfect biomechanical technique. For the purposes of education however, mathematics is probably the worst thing to cram into a young developing mind. Remember, humans learn to move in the womb and then simply keep building from that base for their entire lives. Movement is intuitive to most people and math really never plays a factor in our decision making. When was the last time you stopped before crossing the street and asked which Forces were acting on your body? Probably never, unless you are a biomechanics geek :) So as a coach, I always keep the math principals separate and never pullout equations, unless I am doing it to alter human behaviour in the gym in some way. If that is the case, I only use it in a BF Skinner sort of way and never because I actually think the athlete will understand forces and angles. Here is an example: Gimbal Lock Gimbal Lock is a mathematical concept used in aviation, machine learning, and a million other very technical industries that do not directly correlate to biology or learning. Gimbal Lock is the technical mathematical term for developing your rotations in the wrong “Order of Operations.” For those of you who have seen me coach or watched our videos know that we always say that every skill has an order of operations. This means that if you try to twist before you flip or do a position before you flip or twist you will struggle to do the skill. Your body is a rotating object and unless you apply the forces in the right order of operation you will get Gimbal Lock in the air.

See here for an example - 11 minutes into the video:

As you can see if I do the position first before I create rotation, I automatically 'lock' myself into a pathway of rotation that is limiting my range of motion in the air. To be specific, Gimbal Lock in acrobatics is the failure of the athlete to properly throw the flip and twist rotation on the take-off BEFORE they hit the position. 

In our trainings we always say "FLIP Then Twist Then Position." Of course, this is NOT a universal rule for every skill and each rotation will have a different "Order Of Operation." Generally, "Flip and then Twist " works as a rule of thumb that all athletes can understand no matter your native language or your athlete or their age.  Remember, math is analyzed with equations in the Neocortex, the front of your brain, and that only starts going online in a human at about 7 years old. It is not Fully online until the mid 20's so that means that if anyone under about 16/18 will NOT be able to full grasp mathematical concepts. Coaches, parents and educators make the consistent mistake of believing younger athletes when they ask them if they understand the math concepts. The athlete says "yes" of course because they are trained to do that. How do they get trained to lie?  It's not really a lie (depends on your definition), but every time they show a coach they did not understand a concept, the coach will usually get frustrated and unknowingly express this frustration through body language and even verbal sighs and other cues that young athletes are much better at picking up on than most coaches think. That is because the athlete is still operating on more subconscious circuits in the brain as the Neocortex is still figuring things out. So before the teenage years they are literally nodding along knowing its best to just agree with the coach by saying they 'understand' so the coach does not get frustrated at them and so the lesson can continue. 

So I never use the words Gimbal Lock in training, unless I am talking to an athlete or coach that I know can appreciate this analogy in a way that they understand. But, since gimbals are commonly used in filming, many of the young athletes or influencers today already understand the issue. Again, the reason we want to create analogies that subconsciously are more intuitive to an athlete is because they already have that intuitive knowledge in their brains so you are starting at the point that they already know. Thats a much easier starting point for an athlete and makes the coach's life much easier as well.  No need to get into Euler angles, which is the analytical concept underlying Gimbal Lock. Just make a fun analogy if you can and a simple statement like "Flip Then Twist" and you will get much better results. Then, go talk to your coaching buddies about Euler's equations and frames of reference, but leave it outside of coaching. It just makes it harder! #GRTcertified References:  1) Euler Angles: 2) Gimble Lock Apollo Space Mission: 3)  Gimble Lock Overview: #coaching #training #trampoline #gymnastics #blogpost #gregroetrampoline


bottom of page