Your "core" is really important for stability as well as mobility. Without a strong core your balance is likely to be affected and you are more likely to injure yourself, so it's important to do exercises to challenge your core. Most people think of working their "abs" but there is so much more to it than just that, you need to think about your back muscles, all the abdominals and even glutes in order to be strong and stable. So I have 4 core exercises here the first one easy, the next harder.
Beginner: Lay on ground, feet at a 45 degree angle, make sure feet and knees are a bit apart. Place hands on thighs slowly move up to knees
Expert: Lay on ground, feet at a 45 degree angle, make sure feet and knees are a bit apart. Place hands next to head, slowly curl upper body towards thighs without using momentum or moving feet.
Repeat 10x for 4 reps
Beginner: Lay face down, raise arms/legs off ground slightly, hold up to 30s.
Expert: Lace face down, raise arms/legs much higher off ground, hold up to 30s
Beginner: Lay face down on hands and elbows, make sure back is flat with knees on the ground. Hold pose. 20s-1min
Expert: Lay face down on hands and elbows, make sure hips aren't dropping with either both toes on ground or extend one leg backwards behind. Hold pose. 20s-1min
Lower Body Extension
Beginner: Lay with your hips and upper body on bench, have your legs extended behind you level, hold pose 10-30s
Expert: Lay with stomach/upper body on bench, hips and lower body are extended behind you level, hold pose 10-30s. You can also add weight between your feet to increase the difficulty.