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REALF290 - the problem involves a# The problem involves solving the equations of motion for a double inverted pendulum. The motion is constrained to move in the x-y plane, hence there are no torques about the z-axis. The objective is to compute the spatial motion of these double pendulums over several cycles of their motion and identify any possible behaviors or patterns in this motion.### Understanding the ProblemFirst, I need to understand what a double inverted pendulum is. From what I know, a pendulum is a weight suspended from a fixed point that moves back and sway. When it's inverted, the pendulum is placed upside down, meaning the weight is above the fixed point. A double inverted pendulum would have two pendulums attached to each other, both upside down.Given that the motion is on the x-y plane, I can assume that the setup is in a two-dimensional space, which simplifies the problem as there is no motion in the z direction. This also means there are no torques about the z-axis.### Key Subjects InvolvedThe problem seems to involve physics, particularly mechanics and thermodynamics. It might also involve dynamics and control since the problem is about predicting the behavior of a system.### Starting Steps1. **Set up the system**: I need to set up the double inverted pendulum system in the x-y plane. This includes determining the masses, lengths, and angles of the pendulums.2. **Set up the equations**: I need to use the laws of physics to calculate the equations of motion for the system. This likely involves using Newton's second law and the principles of motion.3. **Compute the motion**: Using the equations, I can compute the motion of the pendulums over several cycles. This might involve doing simulations or calculations to predict the movement.4. **Identify behaviors**: After computing the motion, I can look for any patterns or behaviors in the system. This is where I might identify patterns or trends that could indicate specific behaviors.### ConclusionI think this is a difficult problem that requires applying the principles of physics to predict the dynamics of a double inverted pendulum. It's essential to set up the system correctly and use the correct physics laws to arrive at an accurate solution.
2016年1月3日
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