What is an example of a dangling participle?

An example of a dangling participle is “running at great speed, the dog’s nose started twitching.”

This includes a participial phrase, “running at great speed,” that seems to describe the wrong noun. Although it should describe the dog, the noun that follows the phrase is “the dog’s nose,” making it sound like the nose is running instead of the dog. A better way to phrase this sentence is “as the dog was running at great speed, its nose started twitching.”