- #31
Andreas C
- 196
- 20
Oh, I think I figured it out on my own. I got ##\ddot θ ## in terms of the angular velocity, acceleration, and θ.
How Do You Derive the Cosine of an Integral in Pendulum Motion?
- Context: Undergrad
- Thread starter Andreas C
- Start date
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- Tags
- Derivative Integral
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SUMMARY
The discussion focuses on deriving the cosine of an integral related to the motion of a simple pendulum using Lagrangian mechanics. Participants clarify the distinction between total derivatives and partial derivatives, emphasizing the importance of using the correct notation, particularly in the context of the Euler-Lagrange equation. The final equations derived include the angular acceleration equation, ##\ddot \theta = -\frac{g}{l} \sin \theta##, which is valid for any amplitude of the pendulum's swing. The conversation highlights the significance of understanding harmonic oscillators and their equations of motion.
PREREQUISITES- Lagrangian mechanics
- Partial and total derivatives
- Euler-Lagrange equation
- Basic principles of harmonic motion
- Study the Euler-Lagrange equation in detail
- Learn about the derivation of equations of motion for pendulums
- Explore the concept of harmonic oscillators and their properties
- Investigate the effects of damping on pendulum motion
Students and educators in physics, particularly those focusing on classical mechanics, Lagrangian dynamics, and harmonic motion. This discussion is beneficial for anyone looking to deepen their understanding of pendulum dynamics and related mathematical concepts.
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