In the Ashtanga Yoga version of Sun Salutation B (or Surya Namaskara) there are 18 movements.
As with sun salutation A, the even numbered positions (colored blue) of sun salutation B are done with an inhale. The odd numbered positions are moved into while exhaling.
Initially you may find it difficult to do a whole movement while inhaling or exhaling. While learning, focus on breaking the movement down into steps. Think about each movement before you do it and work towards making each movement smooth.
Here's a summary of all the movements. A detailed "Break Down" follows.
Start by standing with your feet together, knees straight and your weight over your heels (but fronts of your feet still touch the floor). Make the back of your torso and neck feel long (reaching upwards). Arms can be relaxed by your sides or you can put your hands together in front of your heart.
After having learned the A version sun salute, two extra poses that you need to be aware of when doing Sun Salutation B are Chair Pose (Utkatasana), and Warrior 1 (Virabhadrasana 1).
Chair pose is the first and last position of sun salutation B.
While standing, whether you have your feet together or apart, orient your feet so that your toes point straight ahead. Roll your shins outwards so that the outer edge of your foot presses into the floor. At the same time root through the base of your big toe. (Check out "foot exercises" for more information on "foot activation.") Try to keep these actions as you bend your knees. If you do so then your knees should stay at the same width as your feet. If your toes are pointing straight ahead, then your knees should also.
With your arms by your sides activate your feet and practice bending your knees while keeping your feet active.
So that you can stay balanced front to back, practice feeling the fronts and back of your feet. While standing, shift shift your body forwards or back slightly so that your weight is pressing evenly through your heel and your forefoot.
With your feet active and your weight centered, practice bending your knees as you inhale. So that you stay balance reach your hips back and your chest forwards so that your weight continues to press evenly through the fronts and backs of your feet.
To prevent your knees from going to far forwards, you can reach your pelvis back. You can imagine you are trying to reach back to sit down on a chair. To keep your weight centered over your feet, you'll have to balance this action by reaching your ribcage forwards more.
After practicing keeping your feet active and your weight centered, focus on lengthening your spine as you bend your knees. But first practice this while standing.
(Read utkatasana for more on this pose.
While standing, you can practice lifting your ribs away from your pelvis. Do this movement slowly and smoothly while inhaling. Then exhale and relax. Next try to lift your ribs, and once you start inhaling, push your pelvis back and bend your knees.
Sink down (with your pelvis) and lift up (with your ribs) at the same time. As you bend your knees, smoothly lift your arms. Try to use the movement of your hips to initiate the movement of your arms.
When standing up from this pose, as you do at the end of sun salutation b, try to find the same feeling but in reverse. You can imagine using your arms to pull your body upright, or your arms floating down while your body floats up. Try to make the parts of your body work together both while sitting down in the pose and while standing up.
Practice this as many times as you like, inhaling into utkatasana, and exhaling to stand up.
In Warrior 1, one leg is forward and the other leg is back.
Your front knee is bent while your back knee is straight. You reach your arms up above your head. You do this posture twice in Sun Salutation B, once with the right leg forwards and once with the left leg forwards.
To get into this yoga posture while standing, step your left leg back so that your right leg is forwards.
Turn your back foot out about 30 degrees and position your feet so that your heels are about hip width apart (form side to side). If you have no problems with balance then you can also try positioning your heels on the same line.
Start with your knees straight and turn your hips square to the front. As in utkatasana, roll both shins out so that the outer edges of both feet press into the floor. Press down through the base of each big toe.
From here, bend your front knee while keeping your pelvis square to the front. Ideally your front thigh is level with the knee over the middle of the foot (when viewed from the side.) Slide your front foot forwards, or backwards, as you need to.
While holding the pose, inhale and reach your ribs up away from your pelvis. Exhale and relax. Then, as you inhale, reach your arms forwards and up. Try to lead the arm movements with your shoulder blades so that you use both the serratus anterior and trapezius muscles.
Then repeat with your other leg forwards. When doing sun salutation b, you step into warrior 1 from downward dog.
Once you are used to warrior 1, you can now start practicing getting into it from downward dog.
To get your right foot forwards from downward dog, you may find it helpful to first shift your weight to the left. Shift your ribcage to the left so that the weight of your ribcage is on your left hand. Then shift your pelvis to the left so that the weight of it is all on your left foot.
Move your chest and pelvis forwards so that your left shoulder is over your left foot. Lunge your right foot forwards at the same time. Try to get your right foot about even with your left hand.
Turn your left foot out and lift your ribcage. Reach your shoulders forwards and your arms forwards and up.
Notice the position of your feet and make any adjustments necessary. You may have to position your right foot slightly behind your left hand or slightly ahead of it.
Then return to downward dog.
Try the same thing but this time reaching your left foot forwards.
Try to make your movements smooth and controlled. And then try to do them all on one inhale. You may find it helpful if you focus first on making your legs stable (half your inhale) then lift your ribcage and arms (the second half of your inhale.)
When doing sun salutation B, you step back from warrior 1 to Chaturanga Dandasana. Then you do upward dog and downward dog.
To step back to from warrior 1 Chaturanga, first bend down and place your hands on the floor below your shoulders. As you bend forward, let your arms hang down and position them on the floor naturally. Turn the heel of your back foot up. Press into the floor with your hands and then step you front foot back. Lower down to Chaturanga Dandasana. (If you're not yet able to do that pose, then lay down with control.) Then do upward dog and downward dog as you would do in sun salutation a.
To get used to the warrior 1 transition in sun salutation b, you can start from downward dog.
Repeat 100 times!
Just kidding. Once you are used to the above movements, you can put them together into the complete sun salutation b. Remember that this sun salutation starts and finishes with chair pose.
For exercises that can help you improve body awareness in chaturanga dandasana, upward dog and downward dog (as well as wheel pose) check out Yoga Basics.