Formula for balancing an object?

[Tontow]

This is for a game called From The Depths. In this game you make ships out of blocks and those ships then fight each-other. You can also make LUA programming scripts to control those ships, but certain information isn't available to user made scripts.

I could really use some help figuring out and understand the best formula for this because certain information isn't available and the math behind exactly balancing an object is unknown to me.


What we can know automatically:
- The x, y, z location of the craft in the world.
- Where the center of mass is located.
- The maximum size of the ship
- The current pitch and roll and yaw of the ship
- The Gravity at a given altitude ( It will go down the higher up you go, but a little will always be present )
- the Altitude of the ship.
- The Angular Velocity of the ship
- How many points of force are acting on the ship from all directions and the 2 possible directions of that force ( Helicopter blades ).
- We can also know how heavy the ship is, but the user has to manually enter it. ( The ship may get lighter as it takes damage, but there is no way of getting the current weight of the ship. Instead, we know what % health the ship is at and we have to estimate the current weight based on that. )

- The ship and the amount of force that can be exerted on a point is asymmetrical.



What we don't know:
- How much force is available for each point of force. (Users build the helicopter blades, but the game has no way to tell you how much lift/force is available )





With this information:

If I assume that each point of force can exert the same amount of force. How do I tell how much mass is resting on that point?
IE: Think of an asymmetrical shape that has strings attached to it in an asymmetrical pattern and the roll and pitch of the object may or may not be 0. How would you tell how much mass each string is holding up?


How do I tell what percent more force is needed on one side of the craft vs the other to stop the craft from pitching and rolling and yawing?

 

[stapel]

Is what you've posted the full text of the project? What class are you taking, which generated this project? What techniques, formulas, algorithms, programming languages, etc, do you believe the professor expects you to bring to bear?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck? What are your specific mathematical (as opposed to free programming subcontracting) questions?

Please be complete. Thank you!

 

[Tontow]

Is what you've posted the full text of the project? What class are you taking, which generated this project? What techniques, formulas, algorithms, programming languages, etc, do you believe the professor expects you to bring to bear?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck? What are your specific mathematical (as opposed to free programming subcontracting) questions?

Please be complete. Thank you!

I'm not in school right now. This is a personal project that I'm doing for a game that I'm playing.
I never took applied mathematics, but I'm starting to wish I had.



As for the exact questions, see the last part of the fist post:

If you have asymmetrical shape that has strings attached to it in an asymmetrical pattern and the roll and pitch of the object may or may not be 0. How would you tell how much mass each string is holding up?
Note: The force that is holding the object up will always be parallel to the local x, y, or z axis of the object (and not the ground) and the force can be positive or negative.


How do I tell what percent more force is needed on one side of the craft vs the other to stop the craft from pitching and rolling and yawing?
-- I found during my google search on the topic I found http://www.dummies.com/how-to/content/how-to-calculate-rotational-equilibrium.html . But I'm not exactly sure if that is what I need because that is only a static object and I need to account for an object that is rotating.

 

[Tontow]

So during my continued research into this subject I found: Calculating the Center of Thrust on Multirotors

Calculating the Center of Thrust on Multirotors : http://flitetest.com/articles/calculating-the-center-of-thrust-on-multirotors

How would you go about calculating how much mass each rotor is holding up if the object is stationary and the center of gravity is equal to the center of thrust?

 

[Tontow]

Calculating the center of mass is easy if you know how heavy each part is to start with, but what if you don't know how heavy each part is? Or does it matter how heavy each part is when it comes to rotational torque?


IE: (If the weight of each part matters when you try to do something with rotational torque.)

You have an object made of lego blocks. Each block may or may not have a different weight.

If you know the center of mass and the total weight of the object, then what would be the best way to find out how heavy each lego is?
-- Note: I know there can be an infinite number of answers. I need a method of finding the optimum answer. (I would think that it would end up being something like: this block must always be this percent lighter than this block.)