Sensai taught this technique last thursday (May 28th) – unfortunately I did not write it down right away and now that I sat down to capture it the details are fuzzy. The technique is a reversal, starting from a bottom position nage escapes the mount and puts uke in an arm-bar. The figure shows Nage putting an arm bar on Uke’s right hand
Reversal from a bottom mounted position into an arm-bar
To start the technique Nage captures Uke’s right hand – immobilizing it on his chest with his left hand. If Uke is setting up Nage for a technique that starts with a lapel grab – like a deep collar choke – that lapel grab sets up Uke for the technique. So this technique should make for a counter.
As part of setting the escape up Nage makes sure the leg on the side he is arm baring is on Uke’s hip or higher. So if Nage is arm-barring Uke’s right arm then Nage’s right leg is on Uke’s left hip as shown in the figure.
Step two and three
Nage wants to rotate under Uke. Nage does a hip out under Uke. At the same time Nage hooks Uke’s inner thigh with his right hand. This hook lets Nage spin under Uke as opposed to the escaping movement a normal hip out would cause.
Nage raises his outer leg and hooks it over Uke’s neck. Since Nage still has Uke’s arm immobilized Uke is basically a tripod and unstable. So with Uke’s head hooked Nage can flip Uke over onto his back with just the leg hook.
Uke’s shoulder and torso should be touching Nage’s rear, if it is not Nage may have to slide his body forward. Uke’s arm runs through Nage’s groin with Uke’s upper arm resting on Nage’s pelvic bone. Nage’s hip forms the base of a fulcrum formed by Uke’s arm so it is important that the arm is resting on the hip bone and prevented from moving side to side by being sandwiched between Nage’s Legs. Nage sets the technique by arching his hips into the technique – this applies force on the joints using Uke’s arm as a leaver.
The seated arm bar is a joint technique executed on both the shoulder complex and elbow. So the arm needs to be straight so the technique locks out both the elbow joint as well as the shoulder.
Ok, so I just ground through this solution long hand – which sucks because I am fairly sure there was some slick trick I was supposed to have seen here. All the problems in this book are searching for an elegant solution and this one is anything but. I should ask Konrad what I missed when he gets back.
Solve the four equations with four unknowns
…. and it keeps going, and going, and going…. I am really missing something here. This will give me the right solution but *ick*.
The problem is to solve an equation of 5 variables with 5 equations. Making it into a matrix the left side looks like an identity matrix. The first time I solved this I did it long hand – which took forever – then I took another look and saw what they person framing the problem was thinking. Which is cool since this trick should make it easier to attack matrix reduction for some annoying cases.
Solve the system of simultaneous equations
Sum all of the rows to create the new vector S. Then since all the columns of S have the same value it can be normalized so all the values of S are unity. Then by subtracting S from each of the rows (a..e) we create a new matrix M. Multiply M by negative 1 to keep the values at unit as opposed to negative unity and the solution is done. Most important it is done without the page of long hand reduction.
I got like 12 minutes of open mat time.
20 Tekubi-kosa-undo, Tekubi-joho-kosa-undo -> Still not getting these right. Weight not staying under side.
Ok, one of the first equations learned in school is that the area of a right triangle is half the base times the height. Obvious since the base times height gives the area of a rectangle and that is twice the are of the triangle in question. Using calculus though you can say the same thing as:
Area of a right triangle via integration
The pythagorean theorem states that for a right triangle the sum of the squares of the opposite and adjacent sides is equal to the square of the hypotenuse. I used a graphical proof to prove this theorem.
Graphical proof for the pythagorean theorem
I realized that there are things that are important to me other then just martial arts that require constant training if I do not want to loose skills I worked so hard to acquire. One of those things was the ability to describe aspects of the world around me mathematically. I keep reaching back for things I know I once could do with little effort and finding they were either much harder than I remembered – or worse yet now beyond my ability.
So – I am going to try re-working through the basics and working up my skill level again. Hopefully to where I can get better then I once was.