The system that you drew only has two degrees of freedom regardless of what forces you apply to the system. It also isn't clear as to whether you consider the mass a particle or a rigid body. The problem is very different depending on that. If you want a conical pendulum that has forces applied to the particle, then all you need are two generalized coordinates to describe the pendulum's configuration and some definition of force that is applied to the particle.
Jason moorepants.info +01 530-601-9791 On Thu, Aug 18, 2016 at 8:01 AM, Nuno <nmi...@gmail.com> wrote: > Thanks for the input! > > I probably wasn't able to explain it properly, but in this pendulum system > the mass is actuated. Think of it as a differential drive robot with fans > instead of wheels (instead of the mass). The force acting on the x-axis of > the mass frame and the torque about the z-axis of the mass frame are the > result of such structure. > > This makes it different from the normal pendulum where the z-axis is > aligned with the cable. The reference frames would look something like this: > > > <https://lh3.googleusercontent.com/-FFTPk5gauD4/V7XMi5F6nSI/AAAAAAAAAO4/cdpqe8eUdtMOu4CX4FqH3ARI7pxxk9-tQCLcB/s1600/O_76.png> > > > This doesn't make the mass a 6DOF system, since the (x,y,z) of the mass > are dependent of the anchor point position, and in fact in the jupyter > notebook I created > <https://nbviewer.jupyter.org/github/ndevelop/sympy_3D_pendulum/blob/master/3D%20pendulum.ipynb> > I have set only (phi, theta, psi) as the independet generalized coordinates > and (x,y,z) are dependent. > > > That being said I'm sure I'm still making mistakes, so if it was possible > for you to clarify what I'm doing wrong or suggest how to do it properly I > would really appreciate it. > > > Thanks again for all the help, > > Nuno > > > quinta-feira, 18 de Agosto de 2016 às 15:48:35 UTC+1, James Milam escreveu: >> >> To kind of expand on what Jason's saying a 3D pendulum can be completely >> defined using just (x, y, z) and you can deduce the angles from these >> coordinates. In your case the pendulum only has two degrees of freedom (x >> and y for instance and z be calculated because the pendulum has a fixed >> length) and is why Jason suggests using only two generalized coordinates. A >> quadcopter does actually have 6 degrees of freedom and is why it would use >> (x, y, z) in addition to (pitch, roll, yaw). >> > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To post to this group, send email to sympy@googlegroups.com. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/sympy/f110136b-df04-4d04-a06d-d7041ccc789d%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/f110136b-df04-4d04-a06d-d7041ccc789d%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAP7f1AiXDFwKXaEUg73H%2BBDjYqgFguUT7GgAfVAUDZvNyHgtcw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
