To exercise your abs while doing yoga poses it helps to understand what the abdominal muscles do. First of all they connect the ribcage to the pelvis. Second of all you can use them to bend your pull your ribcage down (towards your pelvis) or pull the front of your pelvis up. You can also use them to turn and twist your ribcage relative to your pelvis. And you can use them to keep your lumbar spine stable. That can mean preventing it from bending rearwards.
The yoga poses below include instructions for using the abs. They are arranged as a potential yoga practice. I've included preparation exercises to make some of the poses easier to work towards. You could also use these preparation poses as warm ups.
Yoga poses for the abs include:
Dog pose knee lift, plank pose, crocodile pose (chaturanga dandasana), down dog (for abs),
Standing twist, twisting triangle pose , standing spine flex, standing single leg hip flex, standing forward bend (for abs and hip flexors),
Seated twist, boat pose, lifting up (legs crossed), lifting up with legs straight, dead dog reach, rolling sit up (not pictured above),
Side plank pose variations, half moon variations, side angle pose, triangle pose.
After all of these ab exercises it can help to relax the abs using a pose like a relaxed standing forward bend.
To make ab control easier it can help to add tension to the abs.
To add tension to the abs lift the chest away from the pelvis. With tension added to the abs it can then be easier to use the abs to pull upwards on the front of the pelvis (or twist the ribcage.)
As an example, in warrior 1 you can lift the chest and then use the abs to pull up on the front of the pelvis to help stretch the hip flexors of the back leg.
In poses where it is difficult to lift your chest, you can add tension to the abs by using the Transverse Abdominis to suck the belly inwards.
Transverse Abdominis Relaxed
Transverse Abdominis Active
The transverse abdominis, the innermost layer of abdominal muscle, has horizontal fibers that wrap the waist like a belt. This muscle can be used to pull the belly inwards and at the same time add tension to the obliques and rectus abdominus muscles.
On all fours the abs can be engaged by lifting the knees.
Shoulders Relaxed (Retracted)
Shoulders Active, Knees Lifted
With knees on the floor, spread your shoulder blades to lift your ribcage. Then press your feet down to lift your knees. Pause and then lower and repeat or hold for a few breaths.
Lumbar Lordosis Increased
(abs more relaxed).
Lumbar Lordosis Decreased
(abs more engaged).
From all fours, brace spread your shoulders to lift your ribcage then straighten both knees. Hold this position and tilt your pelvis forwards (so that tailbone moves towards your head). You'll probably find your abs relax a little. Then tilt your pelvis rearwards (so that your pubic bone moves towards your head). This should cause your abs to engage. Notice the change in sensation in your lower back.
Relaxed Crocodile Pose
Active Crocodile (lifted)
Laying prone with elbows bent, push your hands forwards and your feet back to add tension to your arms and legs. Lift your ribcage, pelvis and knees off of the floor. Use your abs to flatten your lower back. Lower and repeat or hold.
This pose is commonly known as chaturanga dandasana.
Shoulders at elbow height.
Lifted all the way up.
Staying lifted you can lift up to the point your shoulders are at elbow height. Or lift all the way up into plank.
Down dog with abs engaged.
In downward dog you can use your abs by moving your chest towards your hands and then by contracting your pubic bone towards your sternum.
Legs strong: pelvis turned relative to feet,
Abs strong: chest turned relative to pelvis.
For a standing twist to exercise the abs, activate your left gluteus maximus if turning right. From there focus on twisting your lumbar spine to the right. To engage your abs then focus on turning the ribcage deeper to the right.
Hand on floor.
For revolved (twisted) triangle start with your hand on the floor. Use your hand to help you twist. Then brace your legs so that your pelvis is stable. Lift your hand and use your abs to twist (or maintain the twist) of your ribcage relative to your pelvis. Twisting to the right you can again engage your left glute.
Pubic bone lifted.
With knees slightly bent lift your tailbone. Then drop your tailbone and lift your pubic bone. Repeat a few times moving slowly and smoothly. This forms the basis for standing hip flexion. With the abs engaged and pulling up on the front of your pelvis your hip flexors have a more stable foundation for flexing the hip.
Hip flex with knee bent (pubic bone lifted).
Hip flex with knee straight (pubic bone lifted).
With weight on one foot, pull up on your pubic bone (or pull upwards and inwards on the front points of your hip bones). Lift the un-weighted knee. Pause and lower or hold and then straighten your knee.
Keep your abs engaged as you straighten your knee.
In the second picture above by chest is being pulled downwards.
Abs and Hip flexors engaged.
While bent forward with hands lifted, contract your abs and the fronts of your hips to bring your chest closer to your thighs.
Lifted leg hip relaxed.
Lifted leg hip actively flexed.
Balancing on one leg while bent forwards, contract your abs, and then pull your lifted leg forwards. Try it first with hands on the floor and then with hands lifted.
Twisting right activate left buttock.
Sitting cross legged with hands in prayer, activate your left gluteus maximus and turn to your right.
For boat pose, lift one knee, turn towards the knee or away from it. Lower and repeat, switching legs each time. You can also do it with the lifted leg straightened.
Using the arms and ribcage as a foundation the abs can be used to help lift the hips and legs. First press down with the arms. (Engage your lats). Lift your hips and pause. Then lift your feet (one at a time is an option).
Engage Arms and Hips.
Lift pelvis and legs.
The same technique can be used for L-Sit. However to prevent cramping of your thighs make sure that you engage your hip muscles, particularly your psoas, prior to lifting.
Lie supine on your back with legs and arms reaching upwards.
To exercise your abs, lift your hips. Then lift your upper back.
One way to cheat in this pose is to grab on to the feet or ankles.
If you find that this pose is too difficult, grab onto your feet, (with hips and upper back lifted), hold for a breath, then leg go of your feet, hold for a breath. Then grab onto your ankles again.
You can grab your feet while exhaling and leg while while inhaling (or vice versa) or as described try to hold each position for an inhale and an exhale.
Grab your legs if too difficult.
From the previous position (relaxed with hips and shoulders on the floor) reach your legs and arms forwards. As your torso comes upright bend your knees to stay balanced. Balance on your butt then return the same way you came up. Repeat 3 or more times. If you have difficulty, grab on to your thighs to begin with, then gradually reduce arm tension and replace with abdominal tension.
Sitting up from the previous position, for side plank, you can start with knees bent. Use your shoulder to lift your chest then press your bottom knee down to lift your hips. Contract the abs on the side of your body closest to the floor. Repeat with knees straight. To also exercise hip flexors you can lift the top knee and straighten it.
Contract bottom side abs.
Contract top side abs.
To turn Half Moon into a yoga poses for your abs do it with the hand lifted. You can exercise the side of the abs closest to the floor by contracting your ribcage towards your standing leg. To exercise the abs on the upper most side focus on bending your waist upwards.
In Side Angle you can reach both arms to the side to work your abs more.
Likewise for Triangle Pose. Instead of resting the bottom hand on the floor or your shin, lift it. To add weight to the pose (and thus strengthen your abs) reach both arms to the side.
Relaxed Forward Bend
To rest your abs while standing you can do a relaxed forward bend. Stand with legs hip width or wider and let your torso hang down. You can hold your elbows or rest your hands on the floor.
As a yoga teacher, I'm constantly exploring new exercises, new ways of doing yoga poses.
There is no single "right way" of doing a yoga pose. Instead, there are options. And the better you are at "feeling" your body, the better you can get at choosing the right option for your body as it is now.
For any technique, the point of practice is to learn feel it and to control it, so that it can be used without thinking about how to use it.
And that is more or less the approach taken in all of my ebooks and videos. They help you to feel your body and control it so that you can work towards using it effectively in anything that you do.