In order to more closely simulate real cycling, there are now stationary bikes that the rider can lean to either side. Currently on Kickstarter, the Austrian-designed Curveplate system allows conventional exercise bikes to do the same thing.
The Curveplate setup consists of two flat-topped rockers made of glass-fiber-reinforced injection-molded plastic.
Utilizing two Velcro polyamide straps on each one, users secure them to the underside of the front and rear base bars (or whatever they're called) on their third-party stationary bike. The system is not designed for use with bicycles mounted on magnetic resistance trainers, as the latter typically have two bars in the rear along with the one in front.
Once the Curveplates are attached, it's reportedly possible to lean the bike by up to 9 degrees to either side without tipping over. Doing so allows riders to rock the bike from side to side as they pedal, more closely simulating actual road riding while also building the user's upper-body strength, core stability and sense of balance.
The system is additionally claimed to reduce butt pain, as the saddle doesn't stay in one unyielding position while the rider pedals. If used with a virtual cycling platform like Zwift, the setup can also be utilized to somewhat mimic the sensation of leaning into turns, although the accompanying feeling of inertia won't be there.
Assuming the Curveplate system reaches production, a pledge of €119 (about the same in US dollars) will get you a complete setup – the planned retail price is $189. It can be seen in use, in the video below.
Cyclists wanting to add some leaning action to their magnetic resistance trainer might instead be interested in KOM Cycling's RPV2 Full-Motion Rocker Plate.
Sources: Kickstarter, Curveplate