Derives equations of motion from energy using generalised coordinates.
Choose generalised coordinates q and form L=T-V; Euler-Lagrange equations d/dt(∂L/∂q')-∂L/∂q=Q give equations of motion without constraint forces. Ideal for complex multi-body systems and robots.
The double pendulum equations are derived neatly with Lagrange.
Lagrangian mechanics gives equations of motion from energy, which is easier than Newton's method for constrained or complicated systems.
Derives equations of motion from energy using generalised coordinates.
Lagrangian mechanics gives equations of motion from energy, which is easier than Newton's method for constrained or complicated systems.
A variable that describes the configuration of a system, such as an angle, chosen to match the constraints so fewer equations are needed.
When constraints are complex or when several bodies interact, since the energy approach avoids solving for each constraint force.
Typical applications include deriving the motion of a double pendulum with constraints, modelling a robot arm with several joints in a simulation and analysing a system with many moving parts linked by constraints.
Study "Topology optimisation" first (topic 100 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Energy-based approach. Handles constraints naturally. Conservation laws from symmetry.
The double pendulum equations are derived neatly with Lagrange.
The next topic is "Hamiltonian mechanics", which builds directly on this one.
It is classed as Advanced in Engineering Mechanics (topic 101 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mechanics.
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