I am sure an elite Mamluk cavalryman was stronger than a modern man sitting before the computer. As most of the reenactors are not soldiers nor athletes, it is very important to build up some strength. For serious reenactment you must put your equipment into action, otherwise it will remain only a costume. In the case of armour and weapons you cannot do it without a level of strength above today’s average. I think not only of the muscles of the arms but the „hidden” ones to, like the muscles of the spinal column to give support while riding in armour, or the neck to withstand the weight of an iron helmet. Your hand and wrist should be as strong as steel to perform controlled saber swings on horseback safely.
So before you get on a horse wearing armour, you should train yourself. I prefer the methods of ancient „body-building”, working only with your body. The best functional book you can read on this subject is Convict Conditioning 1 and 2. For mounted warfare you need functional strength (nobody will see your biceps under the armour:)), strong muscles, joints and tendons. Most of the movements require the whole body, like striking with a sword leaning out of the saddle. For such actions the training program in thoose books are perfect.
I have read in „Training of the Mamluk Faris” that a trainee should start striking the clay with a sword 25 times and increase it by 25 every day till he gets to 1000 sword strike a day. I don’t know whether it is true or not but it bodes incredible strength and endurance.