The bricycle: a bicycle in zero gravity can be balanced or steered but not both. Dong, O.; Graham, C.; Grewal, A.; Parrucci, C.; and Ruina, A. Vehicle System Dynamics, 52(12):1681–1694, December, 2014.
The bricycle: a bicycle in zero gravity can be balanced or steered but not both [link]Paper  doi  abstract   bibtex   
A bicycle or inverted pendulum can be balanced, that is kept nearly upright, by accelerating the base. This balance is achieved by steering on a bicycle. Simultaneously one can also control the lateral position of the base: changing of the track line of a bike or the position of hand under a balanced stick. We show here with theory and experiment that if the balance problem is removed, by making the system neutrally stable for balance, one cannot simultaneously maintain balance and control the position of the base. We made a bricycle, essentially a bicycle with springy training wheels. The stiffness of the training wheel suspension can be varied from near infinite, making the bricycle into a tricycle, to zero, making it effectively a bicycle. The springy training wheels effectively reduce or even negate gravity, at least for balance purposes. One might expect a smooth transition from tricycle to bicycle as the stiffness is varied, in terms of handling, balance and feel. Not so. At an intermediate stiffness, when gravity is effectively zeroed, riders can balance easily but no longer turn. Small turns cause an intolerable leaning. Thus there is a qualitative difference between bicycles and tricycles, a difference that cannot be met halfway.
@article{dong_bricycle:_2014,
	title = {The bricycle: a bicycle in zero gravity can be balanced or steered but not both},
	volume = {52},
	issn = {0042-3114},
	shorttitle = {The bricycle},
	url = {https://doi.org/10.1080/00423114.2014.956126},
	doi = {10.1080/00423114.2014.956126},
	abstract = {A bicycle or inverted pendulum can be balanced, that is kept nearly upright, by accelerating the base. This balance is achieved by steering on a bicycle. Simultaneously one can also control the lateral position of the base: changing of the track line of a bike or the position of hand under a balanced stick. We show here with theory and experiment that if the balance problem is removed, by making the system neutrally stable for balance, one cannot simultaneously maintain balance and control the position of the base. We made a bricycle, essentially a bicycle with springy training wheels. The stiffness of the training wheel suspension can be varied from near infinite, making the bricycle into a tricycle, to zero, making it effectively a bicycle. The springy training wheels effectively reduce or even negate gravity, at least for balance purposes. One might expect a smooth transition from tricycle to bicycle as the stiffness is varied, in terms of handling, balance and feel. Not so. At an intermediate stiffness, when gravity is effectively zeroed, riders can balance easily but no longer turn. Small turns cause an intolerable leaning. Thus there is a qualitative difference between bicycles and tricycles, a difference that cannot be met halfway.},
	number = {12},
	urldate = {2018-07-15},
	journal = {Vehicle System Dynamics},
	author = {Dong, O. and Graham, C. and Grewal, A. and Parrucci, C. and Ruina, A.},
	month = dec,
	year = {2014},
	keywords = {balance, bicycle, bricycle, controllability, dynamics, lean, steer, tricycle},
	pages = {1681--1694}
}
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