Method and apparatus for reactionless rotation

Claim 1

A method for rotating an object mounted on a carrier, wherein the carrier and the object constitute a rotationally free system and have respective centers of mass separated by a separation vector directed from the carrier center-of-mass to the object center-of-mass, comprising rotating the object through a selected angle defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and translating the object so as to displace the object center-of-mass in a translation vector having a translation distance and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance being such that the object is rotated through the selected angle without a substantial counter-rotation of the carrier.

Claim 2

A method for rotating an object mounted on a carrier, wherein the carrier and the object constitute a rotationally free system and have respective centers of mass separated by a separation vector directed from the carrier center-of-mass to the object center-of-mass, comprising rotating the object through a selected angle defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and translating the object so as to displace the object center-of-mass in a translation vector having a translation distance and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance being such that the object is rotated through the selected angle without a substantial counter-rotation of the carrier.

Claim 7

A method for rotating an object pivotally supported on a carriage mounted on a carrier, wherein the carrier, the carriage and the object constitute a rotationally free system, the carrier has a mass M and a carrier center-of-mass, the object has a moment of inertia I about an object center-of-mass, the object and the carriage constitute a subsystem having a mass m and a center-of-mass separated from the carrier center-of-mass by a separation vector having a length L' directed from the carrier center-of-mass to the subsystem center-of-mass, and the subsystem center-of-mass has an initial position on the carrier, the method comprising: rotating the object through a selected angle A about an axis through the object center-of-mass, the selected angle A being defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and simultaneously translating the subsystem so as to displace the subsystem center-of-mass in a translation vector having a translation distance D from the initial position and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance D being determined according to the formula D = A*I*{1/M+1/m}/L, where L is a component length of L' in a direction perpendicular to the translation vector, whereby the object is rotated through the selected angle without a substantial counter-rotation of the carrier.

Claim 8

A method for rotating an object pivotally supported on a carriage mounted on a carrier, wherein the carrier, the carriage and the object constitute a rotationally free system, the carrier has a mass M and a carrier center-of-mass, the object has a moment of inertia I about an object center-of-mass, the object and the carriage constitute a subsystem having a mass m and a center-of-mass separated from the carrier center-of-mass by a separation vector having a length L' directed from the carrier center-of-mass to the subsystem center-of-mass, and the subsystem center-of-mass has an initial position on the carrier, the method comprising: rotating the object through a selected angle A about an axis through the object center-of-mass, the selected angle A being defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and simultaneously translating the subsystem so as to displace the subsystem center-of-mass in a translation vector having a translation distance D from the initial position and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance D being determined according to the formula D = A*I*{1/M+1/m}/L, where L is a component length of L' in a direction perpendicular to the translation vector, whereby the object is rotated through the selected angle without a substantial counter-rotation of the carrier.

Claim 9

An apparatus for rotating an object mounted on a carrier, wherein the carrier and the object constitute a rotationally free system and have respective centers of mass separated by a separation vector directed from the carrier center-of-mass to the object center-of-mass, comprising rotating means for rotating the object through a selected angle defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and translating means for translating the object so as to displace the object center-of-mass in a translation vector having a translation distance and a translation direction such that the mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance being such that the object is rotated through the selected angle without substantial counter-rotation of the carrier.

Claim 10

An apparatus for rotating an object mounted on a carrier, wherein the carrier and the object constitute a rotationally free system and have respective centers of mass separated by a separation vector directed from the carrier center-of-mass to the object center-of-mass, comprising rotating means for rotating the object through a selected angle defined by a rotation vector with a vector direction substantially perpendicular to the separation vector, and translating means for translating the object so as to displace the object center-of-mass in a translation vector having a translation distance and a translation direction such that the mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance being such that the object is rotated through the selected angle without substantial counter-rotation of the carrier.

Claim 16

The apparatus according to claim -2 wherein the object is a telescope or an antenna.

Claim 17

An apparatus for rotating an object on a carrier, comprising: an object to be rotated; carriage means mounted on a carrier for pivotally supporting and moving the object relative to the carrier, wherein the carrier, the carriage means and the object constitute a rotationally free system, the carrier has a mass M and a carrier center-of-mass, the object has a moment of inertia I about an object center-of-mass, the object and the carriage means constitute a subsystem having a mass m and a center-of-mass separated from the carrier center-of-mass by a separation vector having a length L' directed from the carrier center-of-mass to the subsystem center-of-mass, and the subsystem center-of-mass has an initial position on the carrier; rotating means for rotating the object through a selected angle A about an axis through the object center-of-mass, the selected angle A being defined by a rotation vector with a vector direction substantially perpendicular to the separation vector; and translating means for translating the subsystem simultaneously with rotating so as to displace the subsystem center-of-mass in a translation vector having a translation distance D from the initial position and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance D being determined according to the formula D = A*I*{1/M+1/m}/L, where L is a component length of L' in a direction perpendicular to the translation vector, whereby the object is rotated through the selected angle without a substantial counter-rotation of the carrier.

Claim 18

An apparatus for rotating an object on a carrier, comprising: an object to be rotated; carriage means mounted on a carrier for pivotally supporting and moving the object relative to the carrier, wherein the carrier, the carriage means and the object constitute a rotationally free system, the carrier has a mass M and a carrier center-of-mass, the object has a moment of inertia I about an object center-of-mass, the object and the carriage means constitute a subsystem having a mass m and a center-of-mass separated from the carrier center-of-mass by a separation vector having a length L' directed from the carrier center-of-mass to the subsystem center-of-mass, and the subsystem center-of-mass has an initial position on the carrier; rotating means for rotating the object through a selected angle A about an axis through the object center-of-mass, the selected angle A being defined by a rotation vector with a vector direction substantially perpendicular to the separation vector; and translating means for translating the subsystem simultaneously with rotating so as to displace the subsystem center-of-mass in a translation vector having a translation distance D from the initial position and a translation direction such that mathematically crossing the translation vector into the separation vector results in a further vector having the vector direction of the rotation vector, the translation distance D being determined according to the formula D = A*I*{1/M+1/m}/L, where L is a component length of L' in a direction perpendicular to the translation vector, whereby the object is rotated through the selected angle without a substantial counter-rotation of the carrier.