![]() It is mounted to the A/C using a number of rods/lugs. The system is a fairly large mechanical device used on most aircraft (I'm afraid I can't give much more information than that). RE: Solving a 3D force-moment balance using two force application points daniel7campbell (Aerospace) Not sure why you're finding the reactions by two steps, summing the applied then balancing, but i don't think it's Wrong (just Odd). if there is an error in the summing then the reactions won't balance the applied, but there'll still be a solution. I'm sure that given 6 components of load at a point (whether they correctly sum the applied loads or not, i'd thought that an error in this summing might have thrown the math off) then for 2 given points there is a unique solution of 6 reactions components. maybe not, maybe the determinate is zero (maybe 'cause the 6 components are not independent, but rather they are dependent on one another). I'd've thought that since there is a real solution (maybe that's an assumption) that can be determined by "elementary row operations" on a set of simultaneous equations then other matix methods would've worked. RE: Solving a 3D force-moment balance using two force application points rb1957 (Aerospace) 8 Jun 12 11:30īut given pt1 and pt2 then there is only one solution for the 6 force components. now add col2 to col3 and add col 5 to col 6 and finally add row 1 to row 2 to get 0 0 0 0 0 0. Add col2 to col1, add col5 to col4, add row3 to row2 and you get row 2 to become 0 0 -x1 0 0 -x2. So, if you grapple with the first 3 rows as they do to reduce the matrix, you will eventually get all the rows to be 0, thus proving mathematically what I attempted to show above. Similarly, if you have (Fx,0,Mz), you would get an infinity of force vectors at points 1 and 2. For example, take the arbitrary force vector at 0,0 to be (0,0,Mz) then it is clear to me that you can't get a unique Fx1,Fy1, Fx2, Fy2, but an infinity of couples that will produce the Mz. You are asking an arbitrary force vector, (Fx,Fy,Mz) at point at 0,0 to produce unique forces at 2 locations to put the system in equilibrium. ![]() ![]() There is an obvious physical reason for this. Your problem is, as you may know, that the determinant is zero.Īnd that means that the first 3 rows are not independent Substitute into the moment equations to remove Fx1 (and Fy1 and Fz1) so you have three equations and three unknowns (Fx2, Fy2, Fz2) RE: Solving a 3D force-moment balance using two force application points daniel7campbell (Aerospace) i've always reduced the LHS set of equations using elementary row operations. i don't think you can invert the matrix to determine the generalised forces. I think what you're trying to do with it isn't. ('cause forces at 1 and 2 are reacting the sum applied forces) ![]() but i think you should have a -ve sign in there. summing forces and moments at a point due to two generalised forces. ok it took me a little while to realise you're summing the applied forces to get their sum force and sum moments at the origin. ? "I am trying to balance all of the other forces by applying the two additional loads.".
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