英语翻译In bodies possessing axial symmetry (for example,in a homogeneous cylinder),the axis of symmetry is one of the principal axes of inertia .Any two mutually perpendicular axes in a plane at right angles to the axis of symmetry and passing t

英语翻译In bodies possessing axial symmetry (for example,in a homogeneous cylinder),the axis of symmetry is one of the principal axes of inertia .Any two mutually perpendicular axes in a plane at right angles to the axis of symmetry and passing t
英语翻译
In bodies possessing axial symmetry (for example,in a homogeneous cylinder),the axis of symmetry is one of the principal axes of inertia .Any two mutually perpendicular axes in a plane at right angles to the axis of symmetry and passing through the center of mass of the body can be the other two principal axes (Fig.3.9).Thus,in such a body only one of the principal axes of inertia is fixed.
In a body with central symmetry ,i.e.in a sphere whose density depends only on the distance from its center,any three mutually perpendicular axes passing through the center of mass are the principal axes of inertia.Consequently,none of the principal axes of inertia is fixed.
The moments of inertia relative to the principal axes are called the principal moments of inertia of a body.In the general case,those moments differ:I1≠I2≠I3.For a body with axial symmetry ,two of the principal moments of inertia are the same,while the third one,generally speaking ,differs from them:I1=I2≠I3.And,finally,for a body with central symmetry ,all three principal moments of inertia are the same I1=I2=I3 .
Not only a homogeneous sphere,but also,for instance,a homogeneous cube has equal values of the principal moments of inertia.In the general case ,such equally may be observed for bodies of an absolutely arbitrary shape when their mass is properly distributed.All such bodies are called spherical tops.Their feature is that any axis passing through their center of mass has the properties of a free axis and,consequently,none of the principal axes is fixed,as for a sphere.All spherical tops behave the same when they rotate in identical conditions.
Bodies for which I1=I2≠I3 behave like homogeneous bodies of revolution.They are called symmetrical tops.Finally,bodies for which I1≠I2≠I3 are called asymmetrical tops.
If a body rotates in conditions when there is no external action,then only rotation about the principal axes corresponding to the maximum and minimum values of the moment of inertia is stable.Rotation about an axis corresponding to an intermediate value of the moment will be unstable.This signifies that the forces appearing upon the slightest deviation of the axis of rotation from this principal axis act in a direction causing the magnitude of this deviation to grow.When the axis of rotation deviates from a stable axis,the forces produced return the body to rotation about the corresponding principal axis.
We can convince ourselves that what has been said above is true by tossing a body having the shape of a parallelepiped (for example,a match box) and simultaneously bringing it into rotation.We shall see that the body when falling can rotate stably about axes passing through the biggest or smallest faces.Attempts to toss the body so that it rotates about an axis passing through the faces of an intermediate size will be unsuccessful.

英语翻译In bodies possessing axial symmetry (for example,in a homogeneous cylinder),the axis of symmetry is one of the principal axes of inertia .Any two mutually perpendicular axes in a plane at right angles to the axis of symmetry and passing t
具有对称轴的物体,（例如,一个均匀的圆柱体）对称轴是一条惯量轴的主轴.在对称轴的直角平面里,任意两条互相垂直并且穿过物体质心的轴都可以是其他两条主轴(Fig.3.9).因此,在这样一个物体中,只有一条惯量主轴是固定的.
在一个有对称中心的物体里,例如,在一个密度只由中心的距离决定的球体,任意三条穿过质心并且互相垂直的轴就是惯量主轴.因此,没有一条惯量主轴是固定的.
主轴的转动惯量被叫做一个物体的主惯性矩.通常来说,转动惯量是不相等的：:I1≠I2≠I3. .在一个轴对称的物体里,两个转动惯量是一样的,另一个惯量往往是不相等的：I1=I2≠I3.最后,在一个中心对称的物体理,三个主转动惯量都相等的：I1=I2=I3 .
不仅仅是均匀的球体,均匀立方体的主转动惯量值也是相等的.一般情况下,当质量适量分布的时候,这样的相等的物体可能被看做是一个完全任意形状的物体.所有这样的物体被叫做完美球体（球体陀螺）.它们的特点是任意一条穿过它们质心的轴都有虚轴的性质,因此,作为球体,它们没有一条主轴是固定的.在相同的状况下,所有完美球体转动都是相同的.
表现为I1=I2≠I3 的物体是均匀的旋转体.它们被叫做匀称体（匀称陀螺）.表现为 I1≠I2≠I3 的物体是非匀称体（不匀称脱落）.
如果一个物体在没有外力作用的状况下旋转,那么,只有与转动惯量的最大、最小值一致的的主轴的转动才是固定的.与转动惯量的中间值一致的轴的转动是不固定的.这意味着外力会使主轴在某个方向的转动的轻微误差变大.当轴的转动从一个固定轴偏离时,产生的力量使物体回归对应的主轴上转动.
我们可以靠抛一个平行六面体（例如,一个匹配箱）,同时使它旋转,来说服自己上述理论是是正确的.我们会看见物体在下落的时候以穿过最大或最小面为轴稳定旋转.想要抛这个物体使它以穿过中间大小的面（非最大与最小面）为轴转动是不能实现的.
仅供参考,本人非物理专业