http://www.nytimes.com/2008/11/02/sports/playmagazine/112pewarm.html?_r=0
http://well.blogs.nytimes.com/2013/04/03/reasons-not-to-stretch/
http://pilates.about.com/od/whatispilates/a/WhatIsPilates.htm
http://www.***********.com/community/ask_the_experts.asp?q=10
It is important to do warm up exercises, before doing the "hard exercises".
The reason for this is to soften and loosen up muscles and tendons. If you start to do normal exercises before "warming up" (exercise bike, and stretches), you could end up damaging and tearing muscles and tendons, which you do not want.
Same for singing. It is important to do "warm up" exercises to gently loosen up the vocal chords before starting to sing using the full vocal range. Again, damage can be caused to the vocal chords if these are strained.
Pilates was developed in the early 20th century by Joseph Pilates, a physical-culturist from Mönchengladbach, Germany. It is a physical fitness system.
Pilates helps in developing a strong core in improving co-ordination and balance. It helps to build flexibility, muscle strength and helps to build up endurance in the legs, abdominals, arms, hips and back. The exercises concentrate on spinal and pelvic alignment and breathing that helps in strengthening the body's centre.
The exercises start off gently and the intensity increases as the body core strengthens.
There is lots of information on Pilates on the web.
Best wishes.