that can.be done and accounted for on purely dynamical principles, to revert to the subject of bird flight, equipped with the knowledge so obtained.
§ 2. Introductory Remarks (continued).—There is an initial difficulty associated with the study of equilibrium that perhaps has been felt by others who have in the past attempted to investigate the subject ; this difficulty is the indefiniteness of that which is to be investigated.
Whatever kind of thing an aerodrome or aerodone may be, it is evident that when not in flight it is absolutely unconstrained in any one of its degrees of freedom; it is, in fact, free to move bodily in any of the three co-ordinate directions of space, or to rotate about any of the three co-ordinate axes. In any other locomotive appliance we are accustomed to start with some definite limitations; thus a road vehicle is essentially constrained to motions in one plane, and therefore has only three degrees of freedom (i.e., motion in two co-ordinate directions and rotation about one of the co-ordinate axes); a railway locomotive is deprived of all but one of its degrees of freedom, longitudinal motion alone being permitted.
When the aerodrome or aerodone is in free flight, its stability depends upon the limitation that is imposed on its freedom by its functional organs; it must either be deprived of its undesirable degrees of freedom altogether, or its motions permitted in these undesirable degrees must continually react one on another so as to in effect impose a safe limitation in every case ; the only kind of continuous motion that-is permissible being translation in the line of flight. It is the study of these actions and reactions between the forces and couples in and about the co-ordinate axes that forms the basis of the author's present investigations.
The subject may be conveniently approached by a preliminary discussion of the ballasted aeroplane and other simple forms of aerodone; the present chapter is principally devoted to this
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