Herpolhode
Encyclopedia
A herpolhode is the curve traced out by the endpoint of the angular velocity
vector ω of a rigid rotor
, a rotating rigid body
. The endpoint of the angular velocity moves in a plane in absolute space, called the invariable plane, that is orthogonal to the angular momentum
vector L. The fact that the herpolhode is a curve in the invariable plane appears as part of Poinsot's construction
.
The trajectory of the angular velocity around the angular momentum in the invariable plane is a circle in the case of a symmetric top, but it the general case wiggles inside an annulus, while still being concave towards the angular momentum.
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
vector ω of a rigid rotor
Rigid rotor
The rigid rotor is a mechanical model that is used to explain rotating systems.An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space three angles are required. A special rigid rotor is the linear rotor which isa 2-dimensional object, requiring...
, a rotating rigid body
Rigid body
In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...
. The endpoint of the angular velocity moves in a plane in absolute space, called the invariable plane, that is orthogonal to the angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
vector L. The fact that the herpolhode is a curve in the invariable plane appears as part of Poinsot's construction
Poinsot's construction
In classical mechanics, Poinsot's construction is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components...
.
The trajectory of the angular velocity around the angular momentum in the invariable plane is a circle in the case of a symmetric top, but it the general case wiggles inside an annulus, while still being concave towards the angular momentum.