## A Treatise on Gyrostatics and Rotational Motion: Theory and Applications |

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### Other editions - View all

### Common terms and phrases

angular momentum angular speed angular velocity applied approximately axis of figure axis of rotation azimuthal azimuthal motion body-cone centre centroid coincide components cone constant coordinates counter-clock couple curve denote diagram direction cosines disk distance earth ellipsoid elliptic elliptic functions elliptic integrals equations of motion fixed axes fixed point flywheel forces friction function given gives gravity gyroscope gyrostatic action Hence inclination inertia instant instantaneous axis integral kinetic energy limiting circle moment of inertia moving negative obtain oscillation parallel particle path pendulum period perpendicular polhode positive precession precessional principal axes produced quadratic radius result right angles ring rolling roots round ship shown sphere spherical stability steady motion suppose surface symmetry turning vector vertical plane wheel zero αηά ίβ ίη ίΗβ Ιΐιβ ίο νβ ΟΓ οη οί ΤΗβ

### Popular passages

Page 413 - ... energy as part of their thermal energy. The view therefore is plausible that the emission and absorption of radiant energy in band spectra represent changes in this rotational energy. If molecules were really rigid bodies, the application of Bohr's principles to the suggestion would be simple. If / is the moment of inertia of the body about its axis of rotation, to the angular velocity of rotation, the energy of rotation is given by W =\Ia?

Page 33 - ... of a very large one. In the second mode of operating the gyrostat, friction is introduced at the bearings on which the frame of the gyrostat is mounted. With this addition the ship is forcibly prevented from excessive rolling. In the trials of the device it was found that, with the control in operation, the angle of roll of the ship did not exceed 1° in a cross-sea which produced a total swing of 35° when the control was out of action. It is interesting to notice that, contrary to the opinions...

Page 264 - ... frictionless and unacted on by external forces ; whereas, in the present case, friction is the immediate cause of the whirlpool motion. The actual mode of generation of the lateral force will be perhaps better understood, if we suppose small vertical blades to project from the surface of the ball. On that side of the ball where the motion of the blades is up stream, their anterior faces are in part exposed to the pressure due to the augmented relative velocity, which pressure necessarily operates...

Page 494 - ZF ffii sin a) rv. (Coll. Exam.) *' 39. A gyrostat consists of a heavy symmetrical flywheel freely mounted in a heavy spherical case and is suspended from a fixed point by a string of length I fixed to a point in the case. The centres of gravity of the flywheel and case are coincident. Shew that, if the whole revolve in steady motion round the vertical with angular velocity...

Page 33 - ... a ship does not result in the waves breaking over her ; a ship controlled by a gyrostat is, I believe, a dry one. I have here a motor-gyrostat fitted within a skeleton frame representing a ship (Fig. 12). The frame is mounted on two bearings arranged on wooden uprights, and may be made to oscillate on these bearings, so as to imitate the rolling of a ship in a cross-sea. The frame of the gyrostat is mounted on two bearings placed athwart the frame, and a weight is attached to the outside of the...

Page 194 - PE as radius), is equal to the angle between the radii EP and EC, of the two spheres. Hence, by considering the isosceles triangle ECE', we find that the cosine of the obliquity is equal to EE' and we arrive at the preceding expression for E.

Page 32 - ... carried within the ship are smooth, the effect of the gyrostat is to resist the rolling force of the waves, and to bring about a lengthening of the free period of the ship, according to a mathematical theory which, when put in the proper way, is really very simple. Excessive rolling of a ship is due to the cumulative action of the waves, and such cumulative action is only possible where the period of the ship and that of the waves are of about the same order. A large ship has a very long period,...

Page 501 - A ring of wire of radius c rests on the top of a smooth fixed sphere of radius a, and is set rotating about the vertical diameter of the sphere. If the ring is slightly displaced, prove that the motion is unstable if the angular velocity is less than [MT 1885] 3.

Page vi - Yet some, from subtle hints, have got Mysterious light it was a trot But let that pass : they now begun To spur their living engines on : For as whipp'd tops and bandy'd balls, The learned hold, are animals ; So horses they affirm to be Mere engines made by geometry, And were invented first from engines, As Indian Britains were from penguins. So let them be, and, as I was saying, They their live engines ply'd, not staying Until they reach'd the fatal champaign Which th...

Page 218 - The planned inclination of the plane of the orbit to the plane of the earth's equator is 40 deg ±5 deg.