Here is an Article written by Lynda Wallenfels.
"Mountain Biking Articles: Core Strength for Off-Road Athletes
Power in cycling comes from the legs but it cannot be transmitted into the pedals unless you have a strong core platform to push off...Core strength means hips, butt, lower back and abdominals... Integration exercises that work the abdominal, back, hip and butt muscles all at the same time are the best core strengthening exercises.
Tips for all core strengthening exercises:
1. Contract your abdominal muscles throughout all exercises. Think of keeping your belly button pressed into your spine. This keeps you muscles close to your spinal column and provides spinal support.
2. During exercises when both feet are up off the floor, keep your belly button pressed into your spine and your spine pressed into the floor to support your lumbar spine.
3. During exercises when both feet are on the floor, keep your hips and spine in a neutral position.
4. Move fluidly without and throwing and jerking motions.
5. Breathe slowly and smoothly throughout exercises.
6. Add lots of variety into your core training routine.
7. Target your whole core by alternating abdominal, back and side exercises. Use both mobility and stability exercises.
As with all new exercises, start slowly and avoid any movement that causes pain. If you are not confident with your technique, seek the services of a certified personal trainer.
Pillar Ball Twist Get in the push-up position with your feet flat (shoelaces to ball) on top of a stability ball. Place your hands the same width apart they are on the handlebars. Keep your body rigid with legs and feet squeezed together. Rotate your torso to the left turning your belly button to face the wall while rolling onto the side of your left foot. Hold in place for a second and then rotate your feet back to the shoelaces on the ball position with your belly button pointing at floor. Hold for a second and then repeat rotation to the right side. Any butt swinging or bending at the hips or knees is cheating. Make your shoulders and torso do the work. This is a killer exercise for mountain bikers. 10 reps to each side should be tough.
Pull-Ups Do your pull ups palms facing away from the body (like you are holding your handlebars).
Push-Ups Face down, body held rigid in plank position, lower chest to floor and raise up. If you need to, start out building push-up strength on your knees and work up to toes.
Psoas Crunch Kneel on all fours with one end of an elastic exercise-band (swim cords work great here) tied to your right ankle and the other end to an attachment point beyond your feet. Extend your left arm and right leg out and then crunch them in bringing your right elbow towards your left knee. Round your back, exhale and pull your belly button hard up to your spine as you crunch in, hold for two seconds and repeat.
Glute Bridge Lie on your back with your knees bent and feet flat on the floor. Extend one leg and then raise your hips up using the strength of the opposite hip only. Hold for 10 seconds and lower. Repeat 10 times on each side. Keep the hips level and inline with your torso. Weakness will show up by one hip jutting out to the side or dipping lower than the other.
Crunches Lie on your back, knees bent, feet flat on floor. Lift head and shoulders off the floor and then lower. Keep your neck in neutral and don’t pull on your head. Vary tempo. Increase intensity by lifting feet off the floor.
Oblique Crunches Lie on your back, knees bent, feet flat on floor. As you lift your head and shoulders, rotate your torso to the side bringing the opposite knee and hip towards each other. Then lower. Keep your neck in neutral and don’t pull on your head. Alternate sides. Vary tempo.
Side Lifts Lie on your side, legs straight, arms relaxed. Lift shoulders and legs at same time then lower. Vary tempo.
Supermans Lie on the floor face down with your arms extended overhead. Using your core lift your arms, shoulders and legs off the floor and fly like Superman then lower. Vary tempo.
Reverse Crunch Lie on back, press lower back into floor, lift legs with a 90 degree bend at the hips and knees. Curl tailbone off the floor using lower abs then lower while maintaining the 90 degree bend at hips and knees.
Standing Trunk Twist Hold a stick on your shoulders behind head (not on your neck). Twist torso to one side then the other like a periscope. Keep hips facing forward. No rotation in legs and knees.
Hanging Knee Raise Hang from pull up bar or dip station. Contract core muscles. Lift knees as high as you can without throwing them. Control the motion while you raise and lower. Vary tempo.
Seated Knee Raise Sit at the very end of a bench. Lean back slightly. Round your lower back slightly. Lift both feet two inches off floor. Pull one knee towards your chest then extend back to start. Alternate legs. Keep your core contracted and do not let your back arch.
Dumbbell Side Bend Stand with a dumbbell in your right hand. Lower dumbbell down thigh as far as you can without leaning forward or back. Return to upright.
Roll-Ups Lie on your back with your legs straight and arms extended overhead. Exhale as you begin to roll up. Lift your arms, then head, then shoulders. Continue to roll up articulating your spine one vertebrae at a time up and forward. Inhale as you stretch forward keeping your belly button pressed to your spine. Exhale and roll back down slowly with control, exhaling throughout the whole movement. Stretch tall, inhale. Exhale and roll back up. Think of curling yourself forward, stretching then slowly uncurling back down to the mat. Move with a smooth fluid motion at a constant speed. Avoid throwing your body up, or allowing it to flop down. Keep your heels on the floor at all times.
Roll-Over Lie on your back with your arms by your sides and legs held up towards the ceiling. Inhale to prepare. Exhale slowly, contract your lower abs and peel your spine off the mat one vertebra at a time from your tailbone. Inhale when you have lifted as far as you can. Exhale as you lower to the starting position with your legs straight up towards the ceiling. Control the movement avoiding any throwing or jerking. Move fluidly. Do not roll onto the back of the neck, balance on the shoulders instead. Make sure you are lifting from the back of your hips and not simply allowing the weight of your legs to pull you over. Move with your exhale. Only curl your pelvis up as much as your muscle strength will allow.
Roman Chair Back Extensions If you have access to a Roman chair, back extensions are great to build strength. Bend all the way forward and when you lift up, do so only to a neutral spine position. Avoid hyper extending (bending back too much) your spine. Start with 3 X 10 and build up to 3 X 20. I don’t like adding weight to this exercise but prefer adding various rotation movements. As you lift turn your shoulders to the side or try figure of eight rotations with your shoulders.
Swimming Lie on stomach, completely outstretched. Reach your fingertips for the wall on front of you. Hold your head in a neutral spin position (don’t look up). Pull your belly button up in to your spine to activate your transverse abdominis muscle and then bring right arm and left leg up while simultaneously lifting chest off the mat. Switch arms and legs while holding chest up and transverse abdominis muscle tight (just keep your belly button pulled into your spine to do this). Continue beating arms and legs up and down in opposition while holding core strong and stable. Imagine you are balancing on a rock in the water and need to keep the movements controlled so you don’t slip off. Complete 20 beats slowly, 20 beats quickly and another 20 beats slowly with no rest.
Breaststroke Lie on your front with your arms stretched out overhead. Pull your abdominal muscles in towards your spine and keep them locked in throughout the whole exercise. Lift your arms two inches off the ground then arc them around to your sides in a breaststroke fashion while lifting your chest and chin. Hold here for a few seconds, then dive your head down and your arms forward again in a breaststroke fashion back to the start. Breathe as if in water. Inhale as you lift and stroke back and exhale as you dive forward.
Heel-Beats Lie on your front with your arms stretched out overhead. Pull your abdominal muscles in towards your spine and keep them locked in throughout the whole exercise. Straighten your arms and legs and keep them straight throughout the whole exercise. Raise your arms and legs two inches off the floor. Clap your heels 20 times. Rest, stretch and repeat 4 -5 times.
Crawl Lie on your front with your arms stretched out overhead. Pull your abdominal muscles in towards your spine and keep them locked in throughout the whole exercise. Raise your arms and legs two inches off the floor. Hold your left arm and both legs still. Drop only the fingertips of your right hand to the floor and lightly drag them along the floor towards your right shoulder. Raise your elbow up as high as you can towards the ceiling as your arm comes in. Continue dragging your fingertips along the floor and graze your thumb along your side until your arm is straight. Pause here and feel the opposition stretch with your left arm reaching forward and your right arm stretching back. Reverse the finger drag making sure to keep your elbow high. Repeat with left arm. Exhale as you stroke back and inhale as you stroke forward. To reduce the intensity keep your legs on the floor."