1. The problem statement, all variables and given/known data I am trying to establish the the dynamics of an inverted pendulum for further analysis. I understand that this is a well known problem, but the governing equations in various sources are different and make it difficult to keep track of what forces are being applied on the pendulum. I understand there are some assumptions made and hence different models - but in the following source in particular: http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling I am confused and hope someone can clarify the following: 2. Relevant equations In the above link the equations I am having trouble with are (2) and (4) 3. The attempt at a solution In (2) the 2nd and 3rd terms md2x/dt2 and mld2θ/dt2cosθ - are these not one and the same? As in the transversal acceleration ld2θ/dt2 is related to the horizontal component d2x/dt2 by cosθ. If true, why is it counted twice in (2) and if/whether that's an error. In (4) The last term on the left and the 2 terms on the right; again my intuition is suggesting there are repeating terms: mld2θ/dt2 force vector due to angular acceleration, in transversal direction mgsinθ - force due to weight md2x/dt2cosθ - force due to horizontal translation of the point Aren't the latter 2 just constituents of the first? if θ =180° mld2θ/dt2 = -md2x/dt2cosθ = -md2x/dt2 if θ = 90° then mld2θ/dt2 = mgsinθ = mg Hence shouldn't for any θ mld2θ/dt2 = mgsinθ + md2x/dt2cosθ ? In the same equation (4) the terms P and N - are these no repeating as well? Especially since the moment is taken about the hinge, why are these even counted? It also seems like there is a rabbithole going on with the terms md2x/dt2cosθ and mld2θ/dt2cosθ Sorry, I am just very confused as to which forces are being resolved into what directions and why can they be resolved like that. The last 2 terms just seems like they are taking a cosθ of a cosθ component.