Space ship angular deceleration

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Discussion Overview

The discussion revolves around the mathematical modeling of angular deceleration for a spaceship in a simulation context, specifically focusing on how to determine the optimal timing for a spacecraft to switch from accelerating its rotation to decelerating in order to face a specific direction. The scope includes theoretical considerations and practical applications relevant to programming in a space simulation game.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks a mathematical method to calculate when to decelerate a spaceship's rotation based on its current angular velocity and maximum angular acceleration.
  • Another participant describes real-world practices of using short, controlled pulses for rotation initiation and cessation, suggesting that similar methods could be applied in simulations.
  • A participant emphasizes the need for rapid reorientation, proposing that the ship should transition directly from acceleration to deceleration without intermediate steps.
  • One contributor suggests using rotational inertia and torque equations to derive the necessary calculations for stopping the ship at a desired orientation.
  • Another participant proposes a method where torque is applied until the ship reaches halfway to the new orientation, followed by an opposing torque for the remainder of the rotation.
  • A participant raises a concern about ensuring the angular velocity equals zero at the final orientation, noting that starting from a non-zero angular velocity complicates the calculations.
  • One participant compares the problem to linear motion, suggesting that it can be solved using algebraic methods under the assumption of constant torque magnitude.
  • A final contribution provides a simple formula relating time, current angular velocity, and angular acceleration to determine when to decelerate.

Areas of Agreement / Disagreement

Participants express differing views on the best approach to calculate the timing for deceleration, with no consensus reached on a single method. Some propose using algebraic solutions, while others suggest more complex approaches involving torque and inertia.

Contextual Notes

Participants mention various assumptions, such as the constancy of torque and the initial conditions of angular velocity, which may affect the applicability of their proposed methods. The discussion does not resolve these assumptions or the implications of starting from a non-zero angular velocity.

GWilde
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I am programming an addon for a space game/simulation (Kerbal Space Program) and I am looking for some help with a bit of physics.

The part I need a little help with is related to attitude control. If the ship is rotating, is there a mathematical way to calculate when it needs to begin to decelerate rotation to stop facing a certain point? Say I know its current angular velocity and its max angular acceleration?

Ex.
For example ships starts facing direction 1. It begins accelerating its rotation towards directions 2. Then, at the specific calculated point it stops accelerating and begins decelerating so that it stops at direction 2.

In the code I was thinking that I would repeatedly check if at its current angular velocity, if it began decelerating would it stop in time.

Thanks for any help.
 
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For real space objects, generally a short and throttled pulse is used to initiate the rotation, and another short and throttled pulse is used to stop the rotation. A computer with gyro type inputs could do this, but humans were also able to do a good job of this during early space docking test missions. For satellites, internal torques applied to gyro's can be use to reorient them.
 
Thanks, that's cool and all but its not really my question.

I want to do the rotation as fast as possible, so the ship would go directly from accelerating rotation to decelerating rotation. What I need help with is the maths for figuring out when to decelerate rotation.
 
I'm not familiar with doing all the symbolic maths in a post, so I'll have a go with ancient methods.
If you know the ships rotational inertia (I) about the axis if rotation, then you can use T=I*alpha, where T=applied torque (the thruster or whatever), and alpha is the angular acceleration.
Use this with omega = alpha*t, where t is time, omega is angular velocity, and with omega = omega0 + alpha*t where omega0 is initial angular velocity and in this case omega is final angular velocity.
Hence, if you know initial omega0, and I, then calculate a torque T to be applied over time t to make omega zero.
Hope that helps.

Cheers,
Terry
 
For the fastest reorientation, a torque is applied until rotated 1/2 of the way to the new orientation, then an opposing torque of the same magnituded is applied for the second half of the reorientation.
 
How do I factor in that I need the angular velocity to equal zero when the ship will be at the final direction?

Edit: Accelerating for half the time and decelerating for half the time would work for the example of starting from zero rotational velocity, but when implemented the ship might not start from zero rotational velocity so that isn't how I want to do it.
 
Last edited:
It's simialr to linear math. You have an initial angular orientation and initial angular velocity. You want to end up with a final angular orientaion and angular velocity of zero. Assume that the magnitude of the torque is constant and that only the direction changes (if it changes at all, in some cases the solution only required deceleration of the ship). This should only require algebra, not calculus, to solve.
 
GWilde said:
If the ship is rotating, is there a mathematical way to calculate when it needs to begin to decelerate rotation to stop facing a certain point? Say I know its current angular velocity and its max angular acceleration?
time = current angular velocity / angular acceleration
 

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