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Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. See the videos linked from http://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-spacehttps://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-space . But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. See the videos linked from http://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-space . But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. See the videos linked from https://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-space . But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

3 add link to space.stackexchange.com with relevant videos
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Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. See the videos linked from http://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-space . But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. See the videos linked from http://space.stackexchange.com/questions/2954/how-do-astronauts-turn-in-space . But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

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2 Put extra words in title not to confuse with the notion of 'orientation of manifold'
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intuition Intuition as to why the orientation (of a 3D object) is not a conserved quantity?

Say you start off floating in space, in in a fixed position and orientation, with zero linear and angular velocity, with with no external forces. So you are a closed mechanical system. By By twisting your body around,

  • you can't change your linear momentum

    you can't change your linear momentum.

  • you can't change your position (center of mass)

    you can't change your position (center of mass).

  • you can't change your angular momentum

    you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

    you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

intuition as to why orientation is not a conserved quantity?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum
  • you can't change your position (center of mass)
  • you can't change your angular momentum
  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

Intuition as to why the orientation (of a 3D object) is not a conserved quantity?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body around,

  • you can't change your linear momentum.

  • you can't change your position (center of mass).

  • you can't change your angular momentum.

  • you can change your orientation (i.e. rotation)!

The fact that you can change your orientation comes as a surprise to me-- why isn't it conserved like the other three quantities? It's a familiar fact-- cats do it all the time in order to land on their feet, and you can find videos of astronauts doing it on the international space station. But it still seems counterintuitive to me that they can do this while not being able to change the other three quantities. Is there some intuitively clear explanation as to why?

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