Some options: - Earth's surface and orbit are not inertial reference frames. Probably negligible effect. - The flywheel would have mass, and would resist lateral acceleration just because of its momentum. - Maybe some rotational movement is inherent to bipedal locomotion. You mention a 5 degree rotation in the hips which might need to act against the flywheel. - "Dynamics was 18 years ago" - I never took dynamics and am missing something
My question is: WHY would rotational momentum resist lateral acceleration? As far as I know, an object in motion stays in motion unless disturbed by a net unbalanced force. That implies that the flywheel would be able to apply lateral force against the movement of the robot - and if it does, how does it apply that force? As a matter of fact - if that were true, surely there would be implications for airplanes (which have large spinning disks as part of their engine), cars (which have a flywheel in the engine), no? For your specific points: -If Earth's surface and orbit are not inertial reference frames, what reference frame would cause the robot to "have trouble going upstairs" because it has a flywheel? -Yes, they flywheel would have mass. However - would the fact that it's spinning change it's translational inertia? -Rotational IS a part of bipedal locomotion - in one plane. With a single flywheel it is not an issue. So unless the robot is planning to do Olympic-style tilt-starts and tilt-turns when running, that flywheel should not hinder movement as long as it's parallel to the ground.
Maybe I have a more plausible explanation: You have a humanoid robot with a flywheel parallel to the ground for a head. You want him to move forward. To move forward, force is applied by the robot's feet to the ground. This is not happening at the robot's center of mass, so torque is applied to the system. This torque needs to be matched by the flywheel. Maybe that dynamic causes resistance of lateral movement. Airplanes and cars would be mostly exempt because their flywheels don't have much angular momentum, and their torque is overcome in other ways. Airplanes would be doubly exempt because their lateral force is applied near their center of mass. I don't really know anything, and that might have been totally wrong. On the point-by-point: - Earth's surface and orbit are not inertial frames due to the rotation. Lateral motion on earth's surface also implies rotation, as it is a sphere. If the robot wanted to travel 12k miles in any direction, it would need to overcome a half rotation of its flywheel. Also it would constantly want to fall down as the earth rotated. - I just meant the inertia from the flywheel's mass alone. Unless my model above is correct, I agree the mass spinning shouldn't make any difference. - I agree pivoting about the vertical axis is the most obviously important rotation for bipedal motion. But I think the tilt-starts and tilt-turns might be an important part of bipedal motion as well. Since all the transational force is originating at the feet, you need some way to overcome that torque. You can do it by tilting the center of mass in to the direction of travel, or try to compensate with a flywheel, or maybe attach a propeller to the robot's nose.
One question. Why put the flywheel close to the head? (Also I don't think flywheels work that way - most likely it would just look strange, having an ultrastable head - maybe, if built as to make this, have a slouched walk as nothing above the hips except the head is active, resulting in a two-point stabilization - the legs and hips, from the ground, and the gyro head. Cars have a (by my math) 4kg flywheel spinning at, usually, 2000 to 6000 RPM. Planes have (by my estimates - I don't know the exact materials used or exact volume of moving parts, but for a JT9D - the engine used in a lot of 747's, I'm estimating about 25% of moving mass, and the engine weighs 3905 kg - so that alone would be close to 1000kg, so I'm generalizing) upwards of 500 kg of moving parts spinning at upwards of 10 000 RPM. That's a lot of energy, and far from insignificant. How insignificant? The ISS, a space building, uses only a few flywheel systems no larger than a man. -If Earth's surface and orbit are not inertial frames, then what would be the reference frame in which one would have trouble carrying a moving flywheel upwards? Also, 12kmiles - that's about half the circumference of Earth. Let's assume, for pure terror factor, that this machine can run at about 30 mph - faster than the fastest human sprint speed recorded - constantly. To run 12k miles, it would take it about 400 hours. That's a correction of about half a degree an hour - I'm pretty sure that unless you had a supermassive flywheel, the body would have no trouble applying the force necessary to do it. (And if it didn't - we can use gyroscopic precession to apply force to the flywheel to force it to tilt). It most certainly would not fall over, though. -The flywheel shouldn't be more than 10% (if that) of the mass of the machine. It's not especially significant. We humans deal with worse regularly. -Walking and running doesn't create as much torque as you believe. We don't lean forwards just to walk - and we're not doing it that significantly while running. A flywheel would remove the need for that. Tilt-turns maybe - but as previously mentioned, you can apply force to the flywheel directly to make it tilt OR you can give the legs a wide angle of operation and the issue goes away.
> Why put the flywheel close to the head? Just thought it was good imagery. It didn't really matter if it's at the hips or head for that model. > 4kg flywheel spinning at, usually, 2000 to 6000 RPM Assuming a 12 inch flywheel and 6000 RPM, that's roughly equivalent to 4kg moving at 200MPH. Roughly 2% of the kinetic energy of a subcompact moving at 25mph. So I mean, it's not incredibly significant. Anyways, we all took the same physics classes as you. Nobody is arguing with you that rotational energy doesn't effect linear motion in an inertial reference frame in a frictionless vacuum. > We don't lean forwards just to walk We definitely shift our center of mass in the direction of acceleration to accelerate. You don't have to call it leaning, and you could implement a robot whose torso remains upright while shifting its center of mass forwards, but you have to agree with me on this one. I feel like we're having different arguments here. I'm trying to come up with some plausible model of what klienbl00 could have meant when he said a flywheel could resist linear motion. Obviously our high school physics knowledge makes that sound implausible, but I was having fun trying to come up with an explanation other than "no you're wrong". I was frustrated by statements like "the body would have no trouble applying the force necessary" and "doesn't create as much torque as you believe", because I was shooting for an explanation of any possible resistance, not just sufficient resistance to make a flywheel-balanced bipedal robot infeasible.
Sorry about that - I shouldn't have phrased it that way (as it IS an interesting thought experiment).