Don't reinvent the wheel, use it!
One of the most effective tools to help strengthen your core and your shoulder girdle is a device that's been around for at least 50 years. In its basic incarnation, it's called the "ab wheel". That's not as exciting as calling it the "abdominizer", the "super crunch-o-matic", or the "super washboard making, bounce a quarter off your belly, six-pack maker" but it works and it's been working for decades.
What is it? It's just a wheel with handles. A newer version called the "Power Wheel II" adds foot pads so you can also work the front of the core from the feet as well as the hamstrings.
The basic version of the ab wheel exercise is a roll-out from your knees. You'll notice immediately whether or not your core, triceps and lats are weak or strong by how far you can go without falling on your belly. If the roll-out from your knees is not enough of a challenge, you can graduate to the advanced version and roll-out from your feet.
Either way, it's a terrific way to strengthen your core and shoulder girdle. Basic ab wheels can be picked up at most any fitness or sporting goods store and cost $15-20. The Power Wheel II adds foot pedals for even greater exercise versatility. The best price I've found for the Power Wheel II is at Allegro Medical.